<figure><img src="image_1.png" /></figure>

HAL
open science

# The Concept of Homeodynamics in Systems Theory

Hugues Petitjean, Serge Finck, Patrick Schmoll, Alexandre Charlet

► To cite this version:

Hugues Petitjean, Serge Finck, Patrick Schmoll, Alexandre Charlet. The Concept of Homeodynamics in Systems Theory. Complexities, 2025, 1 (1), pp.6. 10.3390/complexities1010006. halshs-05400958

HAL Id: halshs-05400958

https://shs.hal.science/halshs-05400958v1

Submitted on 5 Dec 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Review

# The Concept of Homeodynamics in Systems Theory

Hugues Petitjean <fnref n="1" />, Serge Finck <fnref n="2" />, Patrick Schmoll <fnref n="2" />,* and Alexandre Charlet <fnref n="1" />,*

## Abstract

This review traces the historical evolution, conceptual foundations, and contemporary applications of the term *homeodynamics* across biological, ecological, cognitive, and social systems. Initially coined in the 19th century but largely forgotten, the term re-emerged in the second half of the 20th century as scholars sought to describe dynamic stability in open, self-organizing systems. From Yates's theoretical formalization in biology to Rattan's work in biogerontology and recent applications in psychology and organizational theory, homeodynamics has progressively evolved from a synonym of homeostasis to a distinct systems concept. It now denotes the capacity of complex systems to sustain coherence through transitions between multiple temporary equilibria, integrating feedbacks, bifurcations, and adaptive reconfigurations. By revisiting the term's lineage, this review clarifies its epistemological scope and proposes its use as a heuristic and modeling framework for understanding dynamic stability and regime shifts in living and social systems.

**Keywords:** system theory; complex dynamics; homeostasis; homeodynamics; ball-and-cup model; alternative stable states

## 1. Introduction

This review is dedicated to the uses of the term 'homeodynamics' in the scientific literature. The Google (Ngram NGRAM research: https://books.google.com/ngrams/graph?content=homeodynamics&year_start=1800&year_end=2022&corpus=en&smoothing=3&case insensitive=false (accessed on 23 February 2024)) Viewer application makes it possible to visualize the emergence of this term and the evolution of its usage, both as an adjective (e.g., 'homeodynamic balance') and as a noun ('homeodynamics'), with an initial wave of citations in the 1970s–1980s, followed by a more significant resurgence over the past three decades, and confirmed with the analysis of PubMed and Google Scholar occurrences (Figure 1).

The term homeodynamics has been used for several decades by certain authors, often as an alternative to homeostasis, primarily in biology, but also in other fields. In these contexts, it serves to account for the homeostasis of open and autopoietic systems [1], which do not return to a predefined equilibrium state but nevertheless maintain the factors necessary for their persistence [2].

However, when exploring the uses of this term, it becomes clear that it lacks a precise definition and appears mainly to serve as a way of avoiding the concept of homeostasis, which is sometimes assumed to be limited to closed systems, typically machines, such as W. Ross Ashby's homeostat [3]. Yet the concept of homeostasis is not so restrictive as to require a substitute. As Mathieu Arminjon [4,5] points out, Walter B. Cannon, who

<figure><img src="image_3.png" /></figure>

### check for updates

Academic Editor: José F.F. Mendes

Received: 8 September 2025

Revised: 6 November 2025

Accepted: 18 November 2025

Published: 27 November 2025

**Citation:** Petitjean, H.; Finck, S.; Schmoll, P.; Charlet, A. The Concept of Homeodynamics in Systems Theory. *Complexities* **2025**, *1*, 6.
https://doi.org/10.3390/complexities1010006

**Copyright:** © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Centre National de la Recherche Scientifique, Institute of Cellular and Integrative Neuroscience, Université de Strasbourg, 67000 Strasbourg, France; h petitjean@unistra.fr</footnote>

<footnote n="2">² PSInstitut, 67000 Strasbourg, France; segf@sfr.fr</footnote>

<footnote>* Correspondence: patrick@schmoll.fr (P.S.); acharlet@unistra.fr (A.C.)</footnote>
introduced the concept of homeostasis in 1932 [6,7], was a physician and did not reduce it to Claude Bernard's 19th-century notion of the *milieu intérieur* (Bernard, 1878-1879). On the contrary, Cannon conceived of homeostasis as a coordinated, adaptive process of regulation enabling the organism to maintain functional stability through continual adjustments. Homeostasis is the process that preserves a system's internal conditions in a steady state, minimizing internal change despite external variation. In this first sense, homeodynamics simply echoed this dynamic interpretation of homeostasis, without adding any conceptual novelty [8,9].

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Evolution of the term homeodynamics over time. The x-axis represents calendar years, from 1940 to 2025. The left y-axis is the number of articles containing the term homeodynamic (noun) from Google Scholar (black bars) and the right y-axis is from PubMed (gray bars).</figcaption></figure>

Yet, in more recent theoretical developments, particularly within systems theory and the study of complex adaptive systems, homeodynamics has taken on a broader and more distinct meaning. It no longer refers solely to the maintenance of stability within a single equilibrium but to the persistence of systems that evolve through time by reorganizing their internal relations across multiple attractor states [10,11]. Homeodynamics differs from allostasis and homeorthesis in its scope and level of generality: while allostasis describes adaptive adjustments that restore stability through change (typically short-term physiological regulation), and homeorthesis refers to the maintenance of a dynamic developmental or metabolic trajectory, homeodynamics encompasses both processes within a broader framework [12].

A remarkable phenomenon follows: the term is forgotten, only to be rediscovered by others who, lacking references, sometimes present it as if they had coined it themselves. This review therefore aims to revisit the historical background and various uses of the term, to reattribute its intellectual lineage, and to propose a clear definition. Finally, we will examine whether the term might usefully designate a concept within systems theory.

## 2. Historical Context of the Homeodynamics Term

### 2.1. *Etymology*

The term *homeodynamics* combines the roots “homeo-” and “-dynamic”, respectively, borrowed from the Greek words *δμοιος* *homoios*, meaning “similar” and *δυναμικος* *dynamikos*, meaning “strong” or “powerful”. In its contemporary sense, the term has been constructed with reference to “homeostasis, homeostatic”, primarily to distinguish itself
from them [13]. It thus emphasizes a dynamic rather than a static process, where the
maintenance of “similarity” paradoxically involves change.

## 2.2. *Early Occurrences*

The term *homeodynamics* appears to have first emerged in the title of a medical treatise published in 1869 by Dr. Hilarion Huguet, later reissued in 1887 [13]. In this “*Exposé de médecine homéodynamique*”, the author introduces a “law of functional and curative similarity”, asserting that the efficacy of a remedy lies in the similarity between the remedy’s tendencies and the vital, reactive, or curative functions that the organism naturally employs to counter illness. This gives rise to the etymology “strength of the similar”.

Huguet situated his discussion within the ongoing debate at the same time between
homeopathic and allopathic medicine, proposing that his approach could transcend this
dichotomy. He criticizes the principles of homeopathy, a system invented in 1796 by
Samuel Hahnemann [14], which employs highly diluted substances that, in concentrated
doses, would produce symptoms similar to those of the illness. The term *homeodynamics* is
evidently constructed in reference to *homeopathy* but distinguishes itself by emphasizing
the dynamic interactions between therapeutic interventions and the body’s natural healing
processes. Huguet’s homeodynamics medicine also distances itself from allopathy. It aligns
with the balancing reactions of the body (the term *homeostasis* had not yet been coined) by
supporting natural healing processes rather than opposing the disease with an external
force, which could inadvertently harm natural functions and lead to side effects. After 1890,
and until 1950, the term *homeodynamics* appears only rarely in the Google Books database
of printed sources (https://books.google.com/ngrams, (accessed on 23 February 2024)),
suggesting it fell into relative obscurity during this period.

## 2.3. *Occurrences Associated with the Concept of Homeostasis (1950s)*

In 1926, Walter B. Cannon introduced the concept of homeostasis, which he further elaborated in his seminal work, “The Wisdom of the Body” [6,7]. Following the success of this concept, the adjective *homeodynamics* reappeared in the English-language scientific literature (https://books.google.com/ngrams, (accessed on 23 February 2024)) While not widely used, homeodynamics occurrences are primarily found in biology, particularly in endocrinology: Simon Rodbard (1948), in a study on hypothalamic regulation of body temperature and blood pressure, used homeodynamics term to describe the adaptation of the internal environment under multiple constraints [8]. Later, Henry S. Kaplan (1954) [9] referred to a “homeodynamics equilibrium” in the etiology and pathogenesis of leukemia, highlighting the important role of hormones in maintaining this balance. Frederick Francis Yonkman and Frank L. Mohr (1954) stated that the composition of circulating body fluids reflects the “homeodynamics balance” between factors regulating the production and release of cells by organs and tissues versus forces influencing their elimination [15].

These examples illustrate a usage closely related to homeostasis, with the intention of emphasizing the dynamic nature of a more complex process involving multiple regulatory circuits. The term, still used as an adjective, does not denote a concept significantly different from homeostasis but rather introduces a subtle nuance. Its use in biology was fleeting and largely disappeared by the end of the decade, only to re-emerge in the field some forty years later.

## 2.4. *Disparate Theoretical Formulations in the Field of Human Relations*

The concept of homeostasis was absorbed into the nascent field of cybernetics, facilitating the transposition of related concepts into the social sciences, particularly the study of human collectives such as families and organizations [16]. Within this context, the term *homeodynamics* began to surface among psychotherapists and specialists in education
and training, this time to describe a process extending beyond simple homeostasis [17,18]. However, these mentions were isolated, unconnected, and did not lead to a sustained body of work.

Nathan Ackerman (1908–1971), a significant pioneer in family therapy during the 1950s–1970s, introduced a “homeodynamics principle” as part of his psychodynamic approach to viewing the family as a unit [17]. As a psychiatrist trained in psychoanalysis and influenced by systemic approaches, Ackerman proposed that a healthy family adheres to this principle, combining both homeostasis and change. Homeostatic balance arises from complementary roles and relationships among family members, ensuring structure and stability in the face of uncertainty and familial chaos. This homeostasis is dynamic, in the sense that the family must adapt to change as new situations arise and its members get older (leading to a role inversion) [17]. However, Ackerman’s “homeodynamics principle” was not widely adopted within the systemic therapy field after his death in 1971. It found limited echoes in adult education, where Robert J. Blakely (1915–1994), a journalist, writer, and educator in adult education, titled one of his works “Toward a Homeodynamics Society” [18].

We must mention Martha E. Rogers' work [19], which aimed to establish a theory of nursing based on a holistic conception of care, described as the “science of unitary human beings”. Rogers extended the scope of nursing to encompass any practice promoting human well-being. However, her theory, whose formulation is abstruse, has been criticized, notably by Alan Sokal [20]. Despite this, some contemporary authors continue to identify with her approach in their works [21]. These scattered uses of the term “homeodynamics” in the context of human relations reflect attempts to broaden its application beyond its biological roots. Yet, its adoption has remained limited and episodic.

### 3. The Formation of a Concept in Biology

It took approximately three decades before the term *homeodynamics* was reintroduced and taken up in scientific discussions, beginning with biology at the turn of the millennium.

#### 3.1. *Accounting for the Dynamics of Living Systems*

The reintroduction of the term *homeodynamics* as part of a general theoretical approach to living systems seems to be owed to F. Eugene Yates (1927–2015). His contributions explicitly align with systemic thinking, as evidenced by his organization of major international symposia, such as one on self-organizing systems in Dubrovnik in 1979, which later resulted in a collective volume [22]. In a theoretical article published in 1994, Yates proposed the concept of *homeodynamics* to describe the stability of complex systems that sustain themselves while developing and evolving [22]. Yates drew on the earlier work of Arthur S. Iberall [23], who had used the term *homeokinetics*. Iberall further proposed a “General Theory of Living Systems” that gained limited recognition [23]. In echoing Claude Bernard's “milieu intérieur” theory [24] and Walter Cannon's concept of homeostasis [6,7], Iberall presented his “homeokinetic” theory to account for the dynamic stationarity of living matter. In a systemic perspective, he introduced the notions of cooperative units and dynamic interactivity between these units [25].

Yates adopted and expanded on these ideas, preferring the term *homeodynamics* for its greater accuracy. Finally, he presented it as his personal contribution of a key concept [26], illustrating the phenomenon of words being “reinvented” after being forgotten. Without referencing Yates, the term was revived by Steven P. Rose [27] in a different context—his critique of the excessive enthusiasm for genetics and ultra-Darwinist positions of the time, which viewed life as determined by DNA [26]. Aside, Rose highlighted the work of François Jacob and Jacques Monod (1961), who demonstrated that bacteria initially unable to me-
tabolize lactose could, in a sugar-limited environment, derepress the expression of genes required to synthesize the necessary enzyme [28]. This indicated that genetic programming must exhibit a degree of plasticity to maximize an organism's adaptive capacity to its environment [29]. Rose criticized the implications of homeostasis if interpreted etymologically as remaining the same, arguing instead that constancy is absent in the internal milieu, and change itself is constant. To better capture biological dynamism, Rose proposed replacing *homeostasis* with *homeodynamics*, which he deemed more appropriate.

Mathieu Arminjon, who has written extensively on Walter Cannon and the history of homeostasis, acknowledged that Rose's analysis usefully emphasized the equilibrium disruption inherent in adaptive behaviors [4,5]. However, Arminjon argued that the term *homeostasis* already accounts for such adaptability. As a physician, Cannon understood organisms grow, fall ill, and die. Like many others, Rose reduced the concept of homeostasis to Claude Bernard's "milieu intérieur" and overlooked its full conceptual scope. For [30], an organism's viability is challenged at thresholds that are not predefined but arise from multiple, antagonistic constraints—both endogenous and exogenous. Thus, variability is inherent in the homeostatic model, making Arminjon doubt of the need for a term like *homeodynamics* to address supposed fixed limits in the homeostatic framework (for review, see [12]).

Nonetheless, the terminological debate was underway. Antonio Damasio, who used the term *homeostasis* to describe regulatory processes within the organism and the resulting regularity of life [31], referenced Steven Rose (1997) to note that *homeodynamics* might be more suitable [27]. According to Damasio, the term suggests a process aimed at adjustment rather than a fixed equilibrium point [31]. However, the term remained undefined and indistinct in its application.

## 3.2. *Use of the Term in Biogerontology*

Suresh Rattan, a researcher in biogerontology, adopted the term *homeodynamics* in preference to *homeostasis* also with reference to Steven Rose (1997) and Eugene Yates (1987) to describe the biological mechanisms of aging [32,33]. Rattan developed the role of *hormesis* in delaying biological aging, referring to the stimulation of an organism's biological defenses in response to low doses of toxins or other stress-inducing agents [34]. This mechanism explains how certain natural toxins or pollutants can have opposite effects depending on the dose: high or chronic doses can cause cellular and molecular damage, whereas low, brief exposures can elicit an adaptive response, beneficially stimulating the immune system. Rattan investigates how such *hormesis* effects induced by physical, psychological, or pharmacological stressors can slow aging [34]. Examples include intense physical effort, nutrient deprivation during fasting, exposure to extreme temperatures (e.g., saunas), or controlled changes in breathing patterns (e.g., apnea or hyperventilation).

As early as 2002, Rattan applied the term *homeodynamics*, drawing on Steven P. Rose (1997), to explore the pathways through which certain genes render organisms unable to cope with stress, leading to successive states of equilibrium with reduced internal and external exchange [35]. The term appeared prominently in the title of one of his articles in 2007, discussing homeostasis in the context of aging [32].

Rattan posits that aging is a relative concept that begins when an individual surpasses the normal life expectancy for their species. While genetics dictate the organism's growth, there is no genetic program specifying the precise duration of aging [32]. Growth progresses to a point of stability or maturity after which aging begins. This moment of stability (meaning maturity) marks what Rattan terms the "homeodynamics space". Beyond this point, aging is characterized by the progressive narrowing of the homeodynamics space, increasing vulnerability and the likelihood of age-related diseases.
Rattan identifies three key characteristics of the homeodynamics space: (i) effective stress response, the ability to handle and adapt to stressors; (ii) control and management of damage, the capacity to repair or mitigate cellular and molecular damage; (iii) constant remodeling and adaptation, the continuous adjustments to maintain functionality. The reinforcement of the homeodynamics space can be achieved through hormesis, highlighting the potential of small, beneficial stressors to delay the onset of aging and its associated vulnerabilities.

### 3.3. *The Formalization of the Concept*

David Lloyd, Miguel A. Aon, and Sonia Cortassa (2001) [36], referring to dynamic systems theory applied to biological systems (Rosen, 1970) [37] and the work of Yates [22], introduced the term *homeodynamics* to describe the ability of biological systems to self-organize at bifurcation points where stability is lost. They demonstrated behaviors potentially distinct from homeostasis. While systems may return to an equilibrium state, they can also exhibit complex behaviors with emergent properties, including:

- Transitions between two equilibrium states;

- Threshold crossings;

- Waves and gradients;

- Mutual reinforcements;

- Periodicity and/or chaotic behaviors.

These processes occur across different spatial and temporal scales, from rapid molecular events in membranes to the broader timescales of species evolution.

Lloyd and colleagues [36] provided examples of oscillatory states and periodic movements in biological systems, ranging from neuronal action potentials to menstrual cycles. To represent these dynamics, they introduced a geometric model that revisits the “ball-and-cup” framework (Figure 2). This model conceptualizes systems as navigating among multiple attractor basins, illustrating mutual influences between attractors and the pathways a system might follow among them (for review, see [38]). The concept of bifurcation points was further developed to adopt the terms *homeodynamics* or *dynamic homeostasis* to draw parallels between the behavior of the internet and that of the human brain [39,40]. Their work highlighted the shared self-organizing properties of complex systems, illustrating how such systems adapt and reorganize themselves dynamically under shifting constraints.

This formalization of *homeodynamics* thus extends the concept into a framework for understanding complex, adaptive behaviors beyond biological contexts, opening new avenues for interdisciplinary exploration such as the study of neuronal network plasticity (Figure 3). In multicomponent systems like neuron-astrocyte networks, collective dynamics do not return to a fixed baseline after perturbation. Instead, neuronal activity reorganizes through ongoing feedback interactions with astrocytes and the surrounding network, giving rise to a new functional configuration that preserves global coherence while differing structurally from the previous one. The resulting cumulative activity reflects a homeodynamic regime, in which stability emerges through continuous transformation rather than restoration (Code availability: All the Python 3.1-brian2-2.9.0.4 code for in silico astro-neuronal computation can be found at in following repository: https://github.com/Team-Charlet/Petitjean_et_al_2025, (accessed on 23 February 2024)). From this perspective, neuronal plasticity cannot be adequately described within a homeostatic framework, which implies a return to a prior equilibrium range of values (e.g., firing rates, synaptic weights). Plasticity entails the irreversible reconfiguration of internal parameters such as connectivity, astrocytic modulation, and synaptic efficacy while maintaining the functional integrity of information processing. In other words, neural systems remain stable not by staying the same but by continuously evolving. Indeed, in neuronal-astrocytic
networks, perturbations such as synaptic plasticity or astrocytic feedback do not restore baseline firing rates or connection strengths [41]. Instead, they reorganize internal parameters, giving rise to a new “attractor state” that sustains network function under altered constraints. This process corresponds to Holling’s (1973) and Scheffer’s (1990) concept of alternative stable states [42,43], shifts between basins of attraction that preserve overall viability without returning to previous equilibria including with a change in the parameters of the system, in this case. This is also following Yates (1994) and Lloyd (2001) point of view [10,36], such dynamics are characteristic of homeodynamic systems, where stability emerges from continuous reconfiguration rather than restoration. In conclusion, the regulatory principles governing neural systems correspond to a homeodynamic: stability, defined as the maintenance of functional coherence through transitions across distinct stable configurations: this is achieved through continual reorganization rather than restoration or return to a basal condition, and through the capacity of the system to generate new equilibria that sustain function under perturbation (see Figure 2).

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Homeodynamics and the ball-and-cup model. (A,B). Both diagrams represent “ball-and-cup” model of the dynamic of a system, where the red ball represents the current system state, and the cup-shaped landscape represents the next state reached within some normal range of variation for that system. (A). Diagram of the dynamics of a system visualized as a ball moving across a landscape of troughs and ridges in three dimensions. (B). Diagram of the dynamics of a system visualized as a ball moving across a landscape of troughs and ridges in two dimensions. (C). Normal range of variation can occur through a shift in variables or in parameters of the complex system quantification. (D,E). In the context of the “ball-and-cup” model, hysteresis is the difference between the intensity of two disturbances required to move the red ball from one attraction basin to another and then to return it to its original state. (D). In a case of forward perturbation, the ball initially resides in a shallow basin and a disturbance of intensity ΔX1 is applied, it may be sufficient to push the ball into an adjacent, deeper basin. (E). However, to return the ball to its original basin, a stronger disturbance of intensity ΔX2 is typically required for a reverse perturbation. The difference between these two thresholds, ΔX1 and ΔX2, represents the hysteresis (adapted from [38]).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Homeodynamics in neuroglial networks. (A) Schematic representation of connectivity within a neuron-astrocyte network. Neurons (gray; *n* = 10) are connected to astrocytes with a probability of *p* = 0.1. Astrocytes (green; *n* = 20) are interconnected with one another with *p* = 0.1. The astrocytic network exerts feedback control on neuronal activity, with *p* = 0.5 for astrocyte-neuron coupling. (B) Normalized neuronal activity over time. The trace represents the number of action potentials (APs) per 200 ms bin, normalized to the maximal value (1 = maximum AP count per bin). (C) Intracellular calcium concentration ([Ca²⁺]ᵢ) fluctuations in astrocytes, illustrating distributed signaling and feedback modulation within the glial network. (D) Cumulative astrocytic activity, expressed as the total number of calcium transients over time. The trajectory does not converge to a fixed baseline but evolves through successive plateaus of activity, reflecting a homeodynamic regime. Stability here arises from continuous reorganization of neuron-glia interactions rather than restoration to an initial state. This contrasts with a homeostatic response, which would imply a return to constant range of values. The observed stepwise transitions and quasi-periodic patterns thus exemplify the dynamic stability of an adaptive, evolving system through adaptative feedbacks.</figcaption></figure>

**4. Extension of the Term to Complex Systems in General**

Occurrences of the term *homeodynamics* in biology arise within the framework of, and because of, the application of dynamical systems theory to biological systems. Starting from this usage within a specific domain, it is not surprising that the term eventually extends toward general systems theory, acquiring a broader definition applicable to the dynamics of any complex system.
Again, the Ngram Viewer reveals an interesting trend in the occurrences of the French term *homéodynamique*: it was virtually absent from French-language literature before 2020 but has shown a significant (albeit relative) increase over the past five years. Moreover, its recent use extends beyond biology, appearing in fields such as Martha E. Rogers' nursing theory [19], as well as in transdisciplinary research conducted within the Francophone sphere: among these works, we wish to highlight at least three of them, that have employed the term in different contexts, ranging from psychology to the study of human organizations and finally to the investigation of complex systems [38,44–47].

## 4.1. *Use in Psychology: The Case of Childhood Obesity Inside Family System*

Overweight and obesity have become major global health issues, with a worrying increase among children. Despite numerous intervention programs aimed at prevention and family support, obesity rates continue to rise. This persistence reflects the multifactorial nature of obesity, involving genetic, physiological, psychological, environmental, and sociocultural factors. The condition operates as a self-stabilizing system that maintains a higher weight range through reinforcing feedback loops such as pain and reduced mobility leading to inactivity, which in turn promotes further weight gain [48]. For example, excess weight exacerbates joint problems that discourage physical activity, creating a cycle of decreased energy expenditure and further accumulation of fat mass. Moreover, compensatory physiological mechanisms make it difficult to reverse this state. As detailed by [49], weight loss through dietary restriction typically induces adaptive responses that lower basal metabolic rate and increase appetite, thereby stabilizing body weight around a higher set point. While such mechanisms preserve energy balance, they can also perpetuate the pathological state of obesity. This illustrates how regulatory processes originally serving homeostatic functions can, under chronic conditions, maintain maladaptive equilibria within a complex feedback system.

In this framework, the study by Daria Druzhinenko-Silhan and Patrick Schmoll [44] explicitly presents itself as an example of the application of a homeodynamic approach to the treatment of obesity to surpass systemic feedback loops. For them, the family system often exhibits strong stability around food-related and lifestyle habits that contribute to weight gain. Although obesity manifests as an individual pathology, it must be understood as a global system incorporating biological, psychological, familial, and social processes perhaps even as a pathology of society itself, with economic systems driving the consumption of fatty, sugary, and salty foods [44]. This nested system strongly resists change. Interventions that confront it directly such as informational campaigns, dietary guidelines, or medical and psychological consultations often encounter refusal, missed appointments, or initial engagement without follow-through. Indicators of this systemic inertia include various forms of hysteresis observed at different levels: weight regain after dieting, return to previous eating habits, and relapse into family patterns after initial openness to change [44].

Here, for the authors, approaches targeting homogeneous populations often address the system when it is in a stable, entrenched state, precisely when it is least open to transformation. A dynamic perspective, by contrast, encourages attention to the evolution of the entire system over time, a process marked by successive stable phases: childhood, adolescence, young adulthood, working adulthood. A homeodynamic approach emphasizes the importance for public health policies of intervening during transitional moments, specially near crises, during which the system becomes instable particularly in response to biological, psychological, relational, or social perturbations that accompany life-stage transitions. In the case of obesity, this might include puberty, disruptive family events, or key educational transitions (e.g., from middle school to high school, or high school to university), all of
which can temporarily dislodge the system from its equilibrium and create opportunities
for meaningful change [44].

## 4.2. Homeodynamic in Complex System Dynamics

Petitjean et al. (2025) propose a definition for homeodynamics referring to the dynamic of a system characterized by different stable states through which the system can pass and potentially return, each state obeying locally and temporarily a specific homeostasis, with transitions from one state to another taking place in a discontinuous, nonlinear, manner [38].

The aim of proposing the concept of homeodynamics within a systemic approach is to establish a bridge between very distant fields of research and intervention, from a transdisciplinary perspective that spans biology, ecology, and the social sciences.

Petitjean et al. (2025) homeodynamics frameworks is based on the theory of alternative stable states to establish a conceptual bridge between ecosystem dynamics and bio-psycho-social systems more broadly [38]. Research in ecosystem science led to the formulation of this theory, which posits that ecosystems can exhibit multiple equilibrium states depending on changing environmental conditions. The concept was first introduced by Richard C. Lewontin (1969) [50] and further developed by other scholars, including Crawford S. Holling (1973) [42].

Whereas, in the past, classical ecological models assumed a continuous and gradual evolution of ecosystems in response to environmental change, the theory of alternative stable states highlights the fact that systems often resist external disturbances up to a certain threshold. Beyond that critical point, they undergo abrupt shifts into a new stable state. The system then maintains itself in this new configuration until further disturbances if sufficiently intense either drive it into yet another state, push it back toward the original one, or also reach points of no return (for review, see [51]). However, this return is not symmetrical and involves a phase of resistance, requiring the crossing of a different threshold a phenomenon known as hysteresis. While this definition draws much of its relevance from the theory of alternative stable states, it is not reducible to it. Alternative stable states offer a powerful framework for modeling ecosystems that can shift between multiple equilibrium states, sometimes returning to a previous one.

However, when this perspective is applied to other systems such as psychological development in children (e.g., Jean Piaget's developmental stages 1936 [52,53]), biological aging (e.g., the work of Suresh Rattan [32,34]), or human collectives (e.g., collapse theories) an important nuance emerges: the common observation that living systems, as well as social systems, are mortal. In living organisms or collective systems, development may indeed proceed through distinct stages or plateaus. Yet, unlike in ecosystems modeled with reversible equilibria, these equilibrium states are not truly alternative they are successive. The system is subject to directional forces biological, structural, or historical that constrain it to move forward from one state to the next, without the possibility of return.

In fact, the term homeostasis has played a similar role in the past; however, the authors we have cited all emphasize the need to identify processes that do not seek a return to a fixed equilibrium, but rather an adjustment to internal and external conditions that deviate from equilibrium. From this perspective, while the term *homeostasis* refers to first- and second-generation systemic approaches (first- and second-order cybernetics) [47], which emphasize the system's capacity to maintain a stable state, the term *homeodynamics* refers to a new generation of approaches [26,39,40]. Over the past two decades, these approaches have focused on how systems evolve from one state to another or even transform into entirely new systems. It is also worth emphasizing that in these more recent developments, the notion of homeodynamics has been transposed beyond the physiological domain to describe adaptive processes in organizations, ecosystems, and other complex systems, where
stability emerges through distinct modes of coordination and operates across different levels of organization. In some studies, these adaptive processes can be predicted through a modeling process (for review, see [51]).

# 5. Discussion and Perspectives

## 5.1. Homeodynamics Use as a Heuristic Concept

Beyond its relevance to biological and ecological systems, homeodynamics can also be employed as a heuristic framework to interpret adaptive dynamics in social and organizational systems. We distinguish here between its theoretical use describing stability across multiple attractor states and its heuristic use as a conceptual tool for analyzing how feedback structures and boundary conditions evolve. This distinction extends the classical “ball-and-cup” metaphor by allowing the landscape itself to change over time, providing a more flexible representation of systems that maintain coherence through transformation rather than through return to equilibrium. For example, traditional organizational theories and most analytical or managerial models are derived from the study of mature, relatively stable organizations. These synchronic approaches, centered on large-scale systems, justifiably emphasize homeostasis, the maintenance of internal equilibrium. However, such frameworks inadequately capture the dynamics of small organizations, whose evolution depends strongly on individual actors, particularly their leaders, and where frequent structural changes accompany variations in activity and workforce size [46]. Using homeodynamics as a heuristic framework, Braccini et al. (2025) argue that small organizations develop in a discontinuous, nonlinear manner [45]. Each addition or loss of a key element, such as a collaborator or a major client, reshapes the organization’s equilibrium. Growth thus proceeds through successive crises, each requiring temporary stabilization before renewed expansion. In contrast to homeostasis, which seeks constancy, homeodynamics describes development as a succession of locally stable states, with transitions occurring through abrupt, nonlinear shifts [45]. Its heuristic value lies in drawing attention not only to stable configurations but also, and especially, to critical transitions between them. These thresholds mark phases of systemic instability where the organization becomes more flexible, adaptive, and open to reconfiguration.

## 5.2. Exploring Homeodynamic Putative Mechanism

Understanding what drives transitions between stable states is essential to defining homeodynamics not merely as a conceptual or metaphorical tool but as a dynamic, operative framework. A key contribution of this section is to bridge metaphor and mechanism, specifying the internal logics and dynamical regimes that may underlie homeodynamic processes across systems.

While earlier sections have emphasized the historical and conceptual lineage of the term, including its roots in systems theory and its application across biological, social, and ecological domains, we now turn to the question: *What drives a system from one stable state to another in a homeodynamic framework?* This is not a trivial question, since the homeodynamic model posits not a return to equilibrium but a continual reorganization of the system in response to changing internal or external conditions.

We identify here several putative classes of mechanisms that may underlie such regime-shifting behavior. These mechanisms, while heterogeneous, converge around the idea that systems poised on the edge of instability can reorganize their internal parameters to maintain viability in a changing environment. This is what distinguishes homeodynamics from homeostasis and aligns it with the concept of ultrastability [3], where systems adapt by modifying the parameters of regulation themselves, not just the variables they control.
We propose, without exclusivity or restriction, that the following putative mechanisms
may underlie homeodynamic transitions, including but not limited to:

- *Noise-driven transitions*: In high-dimensional systems with shallow attractor basins, small internal fluctuations can be sufficient to push the system into a new regime. This mechanism has been explored notably in the work of Kaneko and Ikegami (1992) [54], who describe such behavior as *homeochaos*: a weak, high-dimensional form of chaos that facilitates flexible adaptation without losing coherence.

- *Endogenous drift and bifurcation-induced transitions*: Following the work of Ikegami and Suzuki (2010) [55], we consider that slow, endogenous changes in parameters (e.g., metabolic rates, cognitive thresholds, organizational capacities) can gradually steer the system toward a bifurcation point. At that point, even minor perturbations may precipitate a qualitative shift. This mechanism emphasizes the role of internal dynamics, or self-movement, in driving transitions distinct from externally triggered changes.

- *Criticality and “Rein Control”*: Inman Harvey and James Dyke's modeling of Daisyworld systems proposes a regulatory framework they call “Rein Control,” in which the system maintains itself near critical points through local feedback loops. This control allows for spontaneous reconfiguration in response to environmental cues, as the system actively modulates its own stability thresholds. Such a mechanism suggests that homeodynamics may emerge from the tension between stabilizing and destabilizing forces that are themselves under adaptive control [56]. These mechanisms share features with Cannon's original formulation of homeostasis [7].

- *Ultrastability and semantic openness*: Revisiting Ashby's concept of ultrastability, a system may contain a "second-order" feedback loop capable of adjusting its primary regulation rules in response to sustained disturbance [3]. Unlike classical homeostatic systems that return to predefined equilibria, ultrastable systems reorganize their regulatory architecture to persist under novel constraints. In homeodynamic systems, such reorganization often includes historical contingency and semantic openness, i.e., the capacity to generate novel forms of coherence or meaning across scales.

- *Distributed nonlinear interactions with adaptive feedback*: In many biological, ecological, and cognitive systems, collective regime shifts emerge from distributed nonlinear interactions rather than centralized control. Local coupling among units like neurons, agents, or species can generate global reconfigurations, as observed in neural avalanches, ecological collapses, or abrupt social transitions [12,47]. These dynamics reflect emergent properties of network topology, where feedback structure and connectivity determine systemic stability. May's (1973) seminal analysis of randomly connected networks demonstrated that positive feedback loops favor instability, whereas stable cores dominated by negative feedback promote dynamic stability [57]. Later, Paperin et al. (2011) extended this view by linking phase transitions in network connectivity to critical phenomena and dual-phase evolution, through which systems persist by alternating between connected and fragmented states [58]. A neurobiological illustration is provided by Iwasaki et al. (2023) [59], who identified a distributed pain-regulating circuit where oxytocinergic neurons interact through activity-dependent feedbacks to maintain stability via network reconfiguration. Such mechanisms exemplify homeodynamic organization, in which stability arises from continual adaptation rather than fixed equilibria [60] (Figure 3D).

We suggest that these different mechanisms be seen not as competing explanations but
as coexisting dynamical possibilities, whose relevance depends on the particular system un-
der study. Whether in the metabolism of an aging organism, the cognitive development of
a child, or the evolution of an ecological or organizational network, the homeodynamic per-
spective allows us to consider transitions as intrinsic to system viability, not as breakdowns, but as continuous reorganizations through time and information processing.

Thus, the ball-and-cup model, while useful as a heuristic metaphor (see Figure 2), gains theoretical traction only when connected to these dynamical substrates. Future work will benefit from formal modeling efforts that simulate these mechanisms in concrete systems, providing empirical content to the concept of homeodynamics and bridging the gap between descriptive metaphor and predictive theory.

### 5.3. *Perspective and Open Challenges in Modeling Homeodynamic Systems*

While the concept of homeodynamics aims to generalize regime-shifting stability across biological, ecological, and cognitive domains, its operationalization within dynamical systems theory raises several important formal questions. These challenges are particularly relevant to fields grounded in physical modeling, where criteria of stability, energy conservation, and control theory must be met for a system to be mathematically or physically credible [51].

Nonlinear oscillators and high-order maps play a central role in exploring such complex dynamics. In classical systems theory, transitions between regimes, whether periodic, chaotic, or multistable, are often modeled using polynomial vector fields, attractor basins, or discrete-time maps with nonlinear recurrence. In this respect, homeodynamic transitions resemble those observed in generalized Duffing oscillators, Hopf bifurcations, or globally coupled map lattices, which can serve as useful analogs or approximations.

However, a key distinction arises: homeodynamics is not simply an oscillatory regime or chaotic attractor; it implies an ability to reconfigure the regulatory architecture of the system itself, as captured by Ashby's notion of ultrastability. This distinction often places homeodynamic systems outside the scope of conventional dynamical systems defined on fixed manifolds, instead requiring higher-order models that include adaptive feedbacks or even evolving state-spaces (e.g., networks that rewire or reshape their topology based on activity). However, it remains challenging to realize such quantification when considering the ability of the living to self-organize, regulate, rewire and repair [2].

A second challenge concerns energy representation. In physical systems, the stability of a dynamical regime is often supported by an associated energy landscape, whether explicitly defined (in mechanical or thermodynamic systems) or inferred via Lyapunov functions. Homeodynamic systems, however, often operate far from equilibrium and across multiple spatial and temporal scales, which complicates the derivation of energy-based formulations. Anderson et al. (2014) show that such potentials arise naturally in chemical reaction networks, linking stationary stochastic distributions with deterministic stability analysis [61], and quantification of such complex systems can be achieved, for example, using the framework proposed by Fang et al. (2019) in their review, *Nonequilibrium Physics in Biology* [62], or by Mayar et al. (2022) in their work: *Stability and Resilience—A Systematic Approach* [51]. However, these recent advances provide promising avenues for formalizing homeodynamic behavior; significant conceptual and methodological challenges remain. A key open question concerns how to bridge qualitative descriptions of adaptive regulation with quantitative models capable of predicting transitions across scales and domains. Developing such a framework will likely require hybrid approaches that integrate nonlinear dynamics, information theory, and network science, allowing systems to adjust both their parameters and topology in response to perturbations. Another challenge lies in identifying measurable indicators of homeodynamic potential, that is, variables that signal when a system is approaching a critical transition yet still retains the capacity to reorganize rather than collapse. Addressing these issues could lead to a new generation of adaptive dynamical models, capable not only of describing but also of anticipating the
shifting stability of complex living and cognitive systems. In this sense, homeodynamics stands as both a theoretical and computational frontier: it calls for models that evolve with the systems they represent.

**6. Conclusions**

The concept of homeodynamics offers a valuable framework for systemic thinking across disciplinary boundaries, enabling the modeling of complex systems that evolve through both alternative and successive stable states. Whether applied to ecosystems, organisms, or human collectives, homeodynamics provides a lens to study dynamic stability not as a return to equilibrium, but as a process shaped by thresholds, transitions, and constraints.

Beyond its theoretical value, the term invites a broader epistemological shift. Scientific inquiry has long privileged equilibrium states, favoring regularity over rupture and reproducibility over transformation. Yet it is precisely in moments of instability at bifurcations, tipping points, and crises that systems become most susceptible to change. These transitions resist standard modeling approaches, calling instead for longitudinal, qualitative, and case-based methodologies.

By focusing attention on the dynamics of change, homeodynamics rehabilitates neglected scientific methods and opens a transdisciplinary dialog between biology, ecology, psychology, management, and the social sciences. It invites us not only to understand how systems persist but how they evolve.

**Author Contributions:** Conceptualization, H.P. and P.S.; validation H.P., S.F., P.S. and A.C.; data curation, H.P.; writing—original draft preparation H.P., S.F., P.S. and A.C.; writing—review and editing H.P., P.S. and A.C.; visualization H.P. and A.C.; supervision P.S. and A.C.; project administration A.C.; funding acquisition P.S. and A.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Centre National de la Recherche Scientifique contract UPR3212, the Université de Strasbourg contract UPR3212; the NeuroStra Interdisciplinary Thematic Institute of the ITI 2021–2028 program; the FRM Equipe grant EQU202403018071 and the P.S.I group.

**Data Availability Statement:** The original data presented in the study are openly available in https://github.com/Team-Charlet/Petitjean_et_al_2025, (accessed on 23 February 2024).

**Conflicts of Interest:** Authors Serge Finck and Patrick Schmoll are members of the PSInstitut advisory board. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

**References**

1. Varela, F.G.; Maturana, H.R.; Uribe, R. Autopoiesis: The Organization of Living Systems, Its Characterization and a Model. *Curr. Mod. Biol.* **1974**, *5*, 187–196. [CrossRef]

2. Maturana, H.R.; Varela, F.J. *Autopoiesis and Cognition: The Realization of the Living*; Boston Studies in the Philosophy and History of Science; Springer: Dordrecht, The Netherlands, 1980; Volume 42, ISBN 978-90-277-1016-1.

3. Ashby, W.R. *An Introduction to Cybernetics*; Martino Publishing: Mansfield Centre, CT, USA, 2015; ISBN 978-1-61427-765-1.

4. Arminjon, M. Allostasie: Physiologie, Cérébralité et Normativité Sociale. *Bull. D'histoire D'épistémologie Sci. Vie* **2014**, *21*, 87–108. [CrossRef]

5. Arminjon, M. Birth of the Allostatic Model: From Cannon's Biocracy to Critical Physiology. *J. Hist. Biol.* **2016**, *49*, 397–423. [CrossRef]

6. Cannon, W.B.; Cannon, C.J. *The Wisdom of the Body: How the Human Body Reacts to Disturbance and Danger and Maintains the Stability Essential to Life*; Rev. and enl. ed. Renewed; The Norton Library; Norton: New York, NY, USA, 1967; ISBN 978-0-393-00205-8.

7. Cannon, W.B. *The Wisdom of the Body*; W.W. Norton&Co.: New York, NY, USA, 1932.

8. Rodbard, S. Body Temperature, Blood Pressure, and Hypothalamus. *Science* **1948**, *108*, 413–415. [CrossRef]

9. Kaplan, H.S. On the Etiology and Pathogenesis of the Leukemias: A Review. *Cancer Res.* **1954**, *14*, 535–548. [PubMed]
10. Yates, F.E. Order and Complexity in Dynamical Systems: Homeodynamics as a Generalized Mechanics for Biology. *Math. Comput. Model.* **1994**, *19*, 49–74. [CrossRef]

11. Rattan, S.I.S. *Encyclopedia of Biomedical Gerontology*; Elsevier Science & Technology: San Diego, CA, USA, 2019; ISBN 978-0-12-816076-3.

12. Cano-Martínez, A.; Rubio-Ruiz, M.E.; Guarner-Lans, V. Homeostasis and Evolution in Relation to Regeneration and Repair. *J. Physiol.* **2024**, *602*, 2627–2648. [CrossRef]

13. Huguet, H.B.A. *Exposé de Médecine Homéodynamique Basée Sur La Loi de Similitude Fonctionnelle et Appliquée Au Traitement Des Affections Aigües et Chroniques*, 2nd ed.; Delabaye: Paris, France, 1869.

14. Hahneman, S. *Versuch über ein Neues Princip zur Auffindung der Heilkrafte der Arzneisubstanze*; Henricus-Edition Deutsche Klassik Gmbh: Berlin, Germany, 2014; ISBN 3843049734.

15. Yonkman, F.F.; Mohr, F. *Reserpine (Serpasil) and Other Alkaloids of Rauwolfia Serpentina*. *Chemistry, Pharmacology, and Clinical Applications*; New York Academy of Sciences: New York, NY, USA, 1954.

16. Wiener, N. *The Concept of Homeostasis in Medicine*; MIT Press: Cambridge, UK, 1952.

17. Ackerman, N.W. *The Psychodynamics of Family Life: Diagnosis and Treatment of Family Relationships*, 1st ed.; The master work series; Aronson: Northvale, NJ, USA, 1994; ISBN 978-1-56821-341-5.

18. Blakely, J.B. *Toward a Homeodynamics Society*; Syracuse Univ. Press: Syracuse, NY, USA, 1965.

19. Rogers, M.E. *An Introduction to the Theoretical Basis of Nursing*; 18 Print; Davis-Comp: Philadelphia, PA, USA, 1991; ISBN 978-0-8036-7490-5.

20. Sokal, A. Pseudoscience and Postmodernism. Antagonists or Fellow-Travellers? In *Archaeological Fantasies: How Pseudoarchaeology Misrepresents the Past and Misleads the Public*; Fagan, G.G., Ed.; Rootledge: London, UK, 2006; pp. 286–361.

21. Koffi, K. *L'homéodynamique et les Carrières Universitaires non Médicales de la Santé*; l'Harmattan: Paris, France, 2021; ISBN 978-2-343-14416-0.

22. Yates, F.E. *Self-Organizing Systems: The Emergence of Order (Life Science Monographs)*, 1987th ed.; Life Science Monograph; Springer: Berlin/Heidelberg, Germany, 1987.

23. Iberall, A.S. *Toward a General Science of Viable Systems*; McGraw-Hill: Düsseldorf, NY, USA, 1972; ISBN 978-0-07-031672-0.

24. Bernard, C. *Leçons Sur Les Phénomènes de La Vie Communs Aux Animaux et Aux Végétaux*; Baillière&fils.: Paris, France, 1966.

25. Iberall, A.S. *General-Dynamics of the Physical-Chemical Systems in Mammals*; Report to NASA, NASW-1066; NASA: Washington, DC, USA, 1966.

26. Yates, F.E. Homeokinetics/Homeodynamics: A Physical Heuristic for Life and Complexity. *Ecol. Psychol.* **2008**, *20*, 148–179. [CrossRef]

27. Rose, S.P.R. *Lifelines: Biology, Freedom, Determinism*, 1st ed.; Allen Lane: London, UK, 1997; ISBN 978-0-7139-9157-4.

28. Jacob, F.; Monod, J. Genetic Regulatory Mechanisms in the Synthesis of Proteins. *J. Mol. Biol.* **1961**, *3*, 318–356. [CrossRef]

29. Rago, A.; Kouvaris, K.; Uller, T.; Watson, R. How Adaptive Plasticity Evolves When Selected Against. *PLoS Comput. Biol.* **2019**, *15*, e1006260. [CrossRef] [PubMed]

30. Cannon, W.B. Stresses and strains of homeostasis. *Am. J. Med. Sci.* **1935**, *189*, 13–14. [CrossRef]

31. Damasio, A.R. *Looking for Spinoza: Joy, Sorrow, and the Feeling Brain*; HarperCollins Publishers: Boston, MA, USA, 2003; ISBN 978-0-15-602871-4.

32. Rattan, S.I.S. Homeostasis, Homeodynamics, and Aging. In *Encyclopedia of Gerontology*; Elsevier Inc.: Amsterdam, The Netherlands, 2007. [CrossRef]

33. Rattan, S.I.S. Molecular Gerontology: From Homeodynamics to Hormesis. *Curr. Pharm. Des.* **2014**, *20*, 3036–3039. [CrossRef]

34. Rattan, S.I. Ageing, Gerontogenes, and Hormesis. *Indian J. Exp. Biol.* **2000**, *38*, 1–5.

35. Rattan, S.I.S. Biology of Aging and Possibilities of Gerontomodulation. *Proc. Indian Natl. Sci. Acad.* **2003**, *69*, 157–164.

36. Lloyd, D.; Aon, M.A.; Cortassa, S. Why Homeodynamics, Not Homeostasis? *Sci. World J.* **2001**, *1*, 133–145. [CrossRef] [PubMed]

37. Rosen, R. Dynamical System Theory in Biology. In *Stability Theory and Its Applications*; Wiley-Interscience: New York, NY, USA, 1970; ISBN 978-0-471-73550-2.

38. Petitjean, H. Ball-and-cup: Histoire et portée d'un modèle heuristique. *Cah. Systémique* **2025**, *7*, 21–28. [CrossRef]

39. Ikegami, T.; Suzuki, K. From a Homeostatic to a Homeodynamic Self. *Biosystems* **2008**, *91*, 388–400. [CrossRef] [PubMed]

40. Oka, M.; Abe, H.; Ikegami, T. Dynamic Homeostasis in Packet Switching Networks. *Adapt. Behav.* **2015**, *23*, 50–63. [CrossRef]

41. Rojo, D.; Badner, A.; Gibson, E.M. Circadian Control of Glial Cell Homeodynamics. *J. Biol. Rhythms* **2022**, *37*, 593–608. [CrossRef]

42. Holling, C.S. Resilience and Stability of Ecological Systems. *Annu. Rev. Ecol. Syst.* **1973**, *4*, 1–23. [CrossRef]

43. Scheffer, M. Multiplicity of Stable States in Freshwater Systems. *Hydrobiologia* **1990**, *200–201*, 475–486. [CrossRef]

44. Druzhinenko-Silhan, D.; Schmoll, P. L'enfant obèse et sa famille. Une approche homéodynamique. *Cah. Systémique* **2023**, *3*, 5–18. [CrossRef]

45. Braccini, V.; Kaïdi, M.; Schmoll, P. Passages de seuil dans les organisations en croissance et fonction de passeur de l'intervenant. *Cah. Systémique* **2025**, *7*, 45–56. [CrossRef]
46. Braccini, V.; Capelli, F.; Petitjean, H. Naissance et Développement Des Organisations. In *L'Entreprise Inconsciente*; Edition de l'Ill: Strasbourg, France, 2023; pp. 9-24. ISBN 978-2-490874-39-2.

47. Petitjean, H.; Finck, S.; Schmoll, P. Expansion et Effondrement Des Systèmes: Une Discussion Du Concept d'homéostasie. *Bull. D'histoire D'épistémologie Sci. Vie* **2024**, *31*, 85-120. [CrossRef]

48. WHO (World Health Organization). *Obesity and Overweight*; WHO: Geneva, Switzerland, 2023. Available online: https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight (accessed on 11 November 2025).

49. Hall, K.D.; Guo, J. Obesity Energetics: Body Weight Regulation and the Effects of Diet Composition. *Gastroenterology* **2017**, *152*, 1718-1727.e3. [CrossRef]

50. Lewontin, R. The Meaning of Stability. *Q. Rev. Biol.* **1969**, *22*, 13-24.

51. Mayar, K.; Carmichael, D.G.; Shen, X. Stability and Resilience—A Systematic Approach. *Buildings* **2022**, *12*, 1242. [CrossRef]

52. Plante, R. Le phénomène cognitif comme éco-système chez Piaget. *Philosophiques* **1977**, *4*, 245. [CrossRef]

53. Piaget, J. *La Naissance de L'intelligence Chez l'Enfant*; Neuchâtel Suisse, Delachaux et Niestle: Neuchâtel, Switzerland, 1936.

54. Kaneko, K.; Ikegami, T. Homeochaos: Dynamics Stability of a Symbiotic Network with Population Dynamics and Evolving Mutation Rates. *Phys. Nonlinear Phenom.* **1992**, *56*, 406-429. [CrossRef]

55. Suzuki, K.; Ikegami, T. Adaptability and Homeostasis in the Game of Life interacting with the evolved Cellular Automata. *Int. J. Nat. Comput. Res.* **2010**, *1*, 40-50. [CrossRef]

56. Dyke, J.; Harvey, I. Hysteresis and the Limits of Homeostasis: From Daisyworld to Phototaxis. In *Advances in Artificial Life*; Lecture Notes in Computer Science; Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J., Eds.; Springer: Berlin/Heidelberg, Germany, 2005; Volume 3630, pp. 241-251, ISBN 978-3-540-28848-0.

57. May, R.M. Qualitative Stability in Model Ecosystems. *Ecology* **1973**, *54*, 638-641. [CrossRef]

58. Paperin, G.; Green, D.G.; Sadedin, S. Dual-Phase Evolution in Complex Adaptive Systems. *J. R. Soc. Interface* **2011**, *8*, 609-629. [CrossRef] [PubMed]

59. Iwasaki, M.; Lefevre, A.; Althammer, F.; Clauss Creusot, E.; Łapieś, O.; Petitjean, H.; Hilfiger, L.; Kerspern, D.; Melchior, M.; Küppers, S.; et al. An Analgesic Pathway from Parvocellular Oxytocin Neurons to the Periaqueductal Gray in Rats. *Nat. Commun.* **2023**, *14*, 1066. [CrossRef] [PubMed]

60. Baudon, A.; Grelot, V.; Althammer, F.; Wang, K.-Y.; Denis, C.; Ali, S.A.; Yan, Y.; Castillo-Diaz, F.; Piacentini, F.; Creusot, E.C.; et al. Oxytocin $G\alpha_i$ Signaling-Induced Amygdala Astrocytes Processes Retraction Shapes Behavioral Stress Response. *bioRxiv* **2024**. [CrossRef]

61. Anderson, D.F.; Craciun, G.; Gopalkrishnan, M.; Wiuf, C. Lyapunov Functions, Stationary Distributions, and Non-Equilibrium Potential for Chemical Reaction Networks. *Bull. Math. Biol.* **2015**, *77*, 1744-1767. [CrossRef]

62. Fang, X.; Kruse, K.; Lu, T.; Wang, J. Nonequilibrium Physics in Biology. *Rev. Mod. Phys.* **2019**, *91*, 045004. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.