temporal complexity of the order parameter at the phase transition we study a decision making model in a condition where it is equivalent to the two dimensional ising model and we show that at the onset of phase transition it generates temporal complexity namely nonstationary and nonergodic fluctuations we argue that this is a general property of criticality thereby opening the door to the application of the recently discovered phenomenon of complexity matching for an efficient transfer of information to occur a perturbing complex network must share the same temporal complexity as the perturbed complex network

construction of hadamard mathbb z _ 2 mathbb z _ 4 q _ 8 codes for each allowable value of the rank and dimension of the kernel this paper deals with hadamard mathbb z 2 mathbb z 4 q 8 codes which are binary codes after a gray map from a subgroup of direct products of mathbb z 2 mathbb z 4 and q 8 where q 8 is the quaternionic group in a previous work these codes were classified in five shapes in this paper we analyze the allowable range of values for the rank and dimension of the kernel which depends on the particular shape of the code we show that all these codes can be represented in a standard form from a set of generators which can help in understanding the characteristics of each shape the main results we present are the characterization of hadamard mathbb z 2 mathbb z 4 q 8 codes as a quotient of a semidirect product of mathbb z 2 mathbb z 4 linear codes and the construction of hadamard mathbb z 2 mathbb z 4 q 8 codes with each allowable pair of values for the rank and dimension of the kernel

periodically forced ensemble of nonlinearly coupled oscillators from partial to full synchrony we analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling without forcing the system exhibits complicated collective dynamics even for the simplest case of identical phase oscillators due to nonlinearity the synchronous state becomes unstable for certain values of the coupling parameter and the system settles at the border between synchrony and asynchrony what can be denoted as partial synchrony we find that an external common forcing can result in two synchronous states i a weak forcing entrains only the mean field whereas the individual oscillators remain unlocked to the force and correspondingly to the mean field ii a strong forcing fully synchronizes the system making the phases of all oscillators identical analytical results are confirmed by numerics

on fuzzy ordered semigroups abstract the main goal of this paper is to introduce and study some classes of ordered semigroups and to investigate some interesting characterizations theorems of these classes in terms of fuzzy ideals in this respect we characterize weakly regular ordered semigroups for example see theorem 3 4 theorem 3 5 theorem 3 7 intra regular and left weakly regular ordered semigroups see theorem 4 2 theorem 4 4 and semisimple ordered semigroups see theorem 5 5 theorem 5 7 in terms of fuzzy ideals in this regard we define semisimple ordered semigroups and characterize it in terms of fuzzy ideals we also characterize intra regular and weakly regular ordered semigroups in terms of fuzzy ideals

α β ordered linear resolution of intuitionistic fuzzy propositional logic abstract this paper presents an approach for resolution based automated reasoning in intuitionistic fuzzy propositional logic ifl in ifl systems every ifl formula with both a truth degree and a falsity degree at the same time can be transformed into ifl generalized clause based on some equivalent properties in a finite time with assumed thresholds we judge whether each ifl literal of ifl generalized clauses is satisfiable or not according to the ifl literal s satisfiability the ifl literals can be divided into two classes i e similar literals and complementary literals we use the structure of the linear resolution which only has a center line and a side line to restrict the resolution clauses in every resolution procedure ifl framed literals recording information of resolved literals instead of storing them in a memory can be used to reduce the number of possible resolutions and improve the efficiency of the resolution the empty clause can be obtained with layer resolution where the threshold can be changed the soundness and completeness of ordered linear resolution are proved and an illustrative example is given to verify the ordered linear resolution algorithm and demonstrate its effectiveness

on hadamard property of a certain class of finite groups abstract utilizing results of nekrasov and berkovich we investigate hadamard property of a certain class of finite groups

a resolution principle based on first order lattice valued logic lf x abstract in the present paper as a continuous work about resolution principle based on lattice valued propositional logic lp x information sciences 130 2000 1 29 whose algebra of truth values is a relatively general lattice lattice implication algebra lia the lattice valued resolution principle for the corresponding first order lattice valued logic system lf x is focused firstly some concepts about lattice valued resolution principle for lf x are introduced and the herbrand theorem for lf x is proved then an resolution principle which can be used to judge if a first order lattice valued logical formula in lf x is false at a truth valued level i e false is established finally the completeness theorem of this resolution principle and the soundness theorem for the strong resolution are also proved it is hoped that the current work would serve as a foundation for constructing resolution based automated reasoning methods for lattice valued logic capable of dealing with both comparable and incomparable uncertain information

a resolution principle based on lattice valued propositional logic lp x abstract in the present paper resolution based automated reasoning theory in an l type fuzzy logic is focused concretely the resolution principle which is based on lattice valued propositional logic lp x with truth value in a logical algebra lattice implication algebra is investigated finally an resolution principle that can be used to judge if a lattice valued logical formula in lp x is always false at a truth valued level i e false is established and the theorems of both soundness and completeness of this resolution principle are also proved this will become the theoretical foundation for automated reasoning based on lattice valued logical lp x

paraconsistent disjunctive deductive databases abstract databases and knowledge bases could be inconsistent in many ways the semantical characterization of deductive databases that contain disjunctive or indefinite information has been investigated by minker and his co workers 1982 1987 1988 and by henschen and his co workers 1985 1988 in both cases there is one salient feature the databases are assumed to consist of sentences of the form a 1 a n b 1 b m where each a i and each b j is an atom and n 1 thus the database is implicitly assumed to be consistent it is easy to construct a model for any set of such formulas what we study here is a method for reasoning about such databases when they are not necessarily consistent intuitively this occurs when the a i s are restricted not just to atomic formulas but also to negated atoms we use the device of annotated atoms introduced by blair and subrahmanian 1987 1988 to achieve this effect our semantics is closely related to the existing work of newton da costa 1974 1987 whose pioneering work on paraconsistency provides the semantical basis for our formal development

collective phase description of coupled oscillators with general network structure we develop a collective phase description for a population of nonidentical limit cycle oscillators with any network structure undergoing fully phase locked collective oscillations the whole network dynamics can be described by a single collective phase variable we derive a general formula for the collective phase sensitivity which quantifies the phase response of the whole network to weak external perturbations applied to the constituent oscillators moreover we consider weakly interacting multiple networks and develop an effective phase coupling description for them several examples are given to illustrate our theory

exact results for the kuramoto model with a bimodal frequency distribution we analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed the dynamics of this system has been the subject of long standing interest in 1984 kuramoto proposed several conjectures about its behavior ten years later crawford obtained the first analytical results by means of a local center manifold calculation nevertheless many questions have remained open especially about the possibility of global bifurcations here we derive the system s stability diagram for the special case where the bimodal distribution consists of two equally weighted lorentzians using an ansatz recently discovered by ott and antonsen we show that in this case the infinite dimensional problem reduces exactly to a flow in four dimensions depending on the parameters and initial conditions the long term dynamics evolves to one of three states incoherence where all the oscillators are desynchronized partial synchrony where a macroscopic group of phase locked oscillators coexists with a sea of desynchronized ones and a standing wave state where two counter rotating groups of phase locked oscillators emerge analytical results are presented for the bifurcation boundaries between these states similar results are also obtained for the case in which the bimodal distribution is given by the sum of two gaussians

mean field approximation of two coupled populations of excitable units the analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of n stochastic excitable units each is performed by studying an approximate system obtained by replacing each population with the corresponding mean field model in the exact system one has the units within an ensemble communicating via the time delayed linear couplings whereas the interensemble terms involve the nonlinear time delayed interaction mediated by the appropriate global variables the aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system governed by a set of 4n stochastic delay differential equations for the microscopic dynamics can accurately be reproduced by a flow containing just four deterministic delay differential equations which describe the evolution of the mean field based variables in particular the considered issues include determining the parameter domains where the stationary state is stable the scenarios for the onset and the time delay induced suppression of the collective mode as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state we show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations like those with symmetrical or asymmetrical interpopulation couplings

transition from spatial coherence to incoherence in coupled chaotic systems we investigate the spatio temporal dynamics of coupled chaotic systems with nonlocal interactions where each element is coupled to its nearest neighbors within a finite range depending upon the coupling strength and coupling radius we find characteristic spatial patterns such as wavelike profiles and study the transition from coherence to incoherence leading to spatial chaos we analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations identifying a critical coupling strength and a scaling relation of the coherent profiles to demonstrate the universality of our findings we consider time discrete as well as time continuous chaotic models realized as a logistic map and a r ossler or lorenz system respectively thereby we establish the coherence incoherence transition in networks of coupled identical oscillators

the mathematics of asymptotic stability in the kuramoto model now a standard in nonlinear sciences the kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators while its basic phenomenology has been sketched in early works the corresponding rigorous validation has long remained problematic and was achieved only recently this paper reviews the mathematical results on asymptotic stability of stationary solutions in the continuum limit of the kuramoto model and provides insights into the principal arguments of proofs this review is complemented with additional original results various examples and possible extensions to some variations of the model in the literature

chimeralike states in two distinct groups of identical populations of coupled stuart landau oscillators we show the existence of chimeralike states in two distinct groups of identical populations of globally coupled stuart landau oscillators the existence of chimeralike states occurs only for a small range of frequency difference between the two populations and these states disappear for an increase of mismatch between the frequencies here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population we also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states an imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population i and synchronized oscillations in population ii also the existence of chimera state is independent of the increase of frequency mismatch between the populations we also find the coexistence of different dynamical states with respect to different initial conditions which causes multistability in the globally coupled system in the case of nonlocal coupling the system does not show multistability except in the cluster state region

complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling we consider large populations of phase oscillators with global nonlinear coupling for identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self organized quasiperiodicity in this state phases of all units differ yet the population is not completely incoherent but produces a nonzero mean field the frequency of the latter differs from the frequency of individual units here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies we demonstrate numerically and describe theoretically i states of complete synchrony ii regimes with coexistence of a synchronous cluster and a drifting subpopulation and iii self organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it we analyze transitions between different states with the increase of the coupling strength in particular we show that the mean field arises via a discontinuous transition for a further illustration we compare the results for the nonlinear model with those for the kuramoto sakaguchi model

fronts and bumps in spatially extended kuramoto networks abstract we consider moving fronts and stationary bumps in networks of non locally coupled phase oscillators fronts connect regions of high local synchrony with regions of complete asynchrony while bumps consist of spatially localised regions of partially synchronous oscillators surrounded by complete asynchrony using the ott antonsen ansatz we derive non local differential equations which describe the network dynamics in the continuum limit front and bump solutions of these equations are studied by either freezing them in a travelling coordinate frame or analysing them as homoclinic or heteroclinic orbits numerical continuation is used to determine parameter regions in which such solutions exist and are stable

synchronization of dynamical hypernetworks dimensionality reduction through simultaneous block diagonalization of matrices we present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems we are able to reduce the dimensionality of the problem by using simultaneous block diagonalization of matrices we obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower dimensional problems and test the predictions of our low dimensional analysis through numerical simulations under certain conditions this technique may yield a substantial reduction of the dimensionality of the problem for example for a class of dynamical hypernetworks analyzed in the paper we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2 we apply our reduction technique to a number of different examples including the class of undirected unweighted hypermotifs with 3 nodes

l valued propositional logic l vpl in this paper two types of gradational l type lattice valued propositional logic l v p l with truth values in a lattice implication algebra are introduced and some fundamental questions of them such as semantics syntax and compactness are investigated and where the l type a soundness theorem a b completeness theorem a b consistent theorem and a b q deduction theorem are also proved

cocyclic hadamard matrices and hadamard groups are equivalent abstract in this paper we prove that the concepts of cocyclic hadamard matrix and hadamard group are equivalent a general procedure for constructing hadamard groups and classifying such groups on the basis of isomorphism type is given to illustrate the ideas cocyclic hadamard matrices over dihedral groups are constructed and the corresponding hadamard groups classified

a resolution like strategy based on a lattice valued logic as the use of nonclassical logics becomes increasingly important in computer science artificial intelligence and logic programming the development of efficient automated theorem proving based on nonclassical logic is currently an active area of research this paper aims at the resolution principle for the pavelka type fuzzy logic 1979 pavelka showed that the only natural way of formalizing fuzzy logic for truth values in the unit interval 0 1 is by using the lukasiewicz s implication operator a spl rarr b min 1 1 a b or some isomorphic forms of it hence we first focus on the resolution principle for the lukasiewicz logic l sub spl aleph with 0 1 as the truth valued set some limitations of classical resolution and resolution procedures for fuzzy logic with kleene implication are analyzed then some preliminary ideals about combining resolution procedure with the implication connectives in l sub spl aleph are given moreover a resolution like principle in l sub spl aleph is proposed and the soundness theorem of this resolution procedure is also proved second we use this resolution like principle to horn clauses with truth values in an enriched residuated lattice and consider the l type fuzzy prolog

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

globally clustered chimera states in delay coupled populations we have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically and aperiodically and become unstable depending upon the value of coupling delay we also find that the coupling delay induces frequency suppression in the desynchronized group we provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena

effects of nonresonant interaction in ensembles of phase oscillators we consider general properties of groups of interacting oscillators for which the natural frequencies are not in resonance such groups interact via nonoscillating collective variables like the amplitudes of the order parameters defined for each group we treat the phase dynamics of the groups using the ott antonsen ansatz and reduce it to a system of coupled equations for the order parameters we describe different regimes of cosynchrony in the groups for a large number of groups heteroclinic cycles corresponding to a sequential synchronous activity of groups and chaotic states where the order parameters oscillate irregularly are possible

on the phase reduction and response dynamics of neural oscillator populations weundertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli recalling and extending results from the literature we compute phase response curves prcs valid near bifurcations to periodic firing for hindmarsh rose hodgkin huxley fitzhugh nagumo and morris lecar models encompassing the four generic codimension one bifurcations phase density equations are then used to analyze the role of the bifurcation and the resulting prc in responses to stimuli in particular we explore the interplay among stimulus duration baseline firing frequency and population level response patterns we interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions

ili ideals and prime li ideals in lattice implication algebras the notions of ili ideals and maximal li ideals of lattice implication algebras are introduced respectively the properties of ili ideals prime li ideals and maximal li ideals are investigated several characterizations of ili ideals and prime li ideals are given the extension theorem of ili ideals is obtained the relations between ili ideals and li ideals between ili ideals and implication filter between prime li ideals and maximal li ideals between prime li ideals and ili ideals between maximal li ideals and ili ideals between maximal li ideals and li ideals and between prime li ideals and li ideals are investigated respectively some classes of lattice implication algebras are characterized by their ili ideals respectively prime li ideals maximal li ideals

controlling synchronous patterns in complex networks although the set of permutation symmetries of a complex network could be very large few of them give rise to stable synchronous patterns here we present a general framework and develop techniques for controlling synchronization patterns in complex network of coupled chaotic oscillators specifically according to the network permutation symmetry we design a small size and weighted network namely the control network and use it to control the large size complex network by means of pinning coupling we argue mathematically that for any of the network symmetries there always exists a critical pinning strength beyond which the unstable synchronous pattern associated to this symmetry can be stabilized the feasibility of the control method is verified by numerical simulations of both artificial and real world networks and demonstrated experimentally in systems of coupled chaotic circuits our studies show the controllability of synchronous patterns in complex networks of coupled chaotic oscillators

partial synchronization and partial amplitude death in mesoscale network motifs we study the interplay between network topology and complex space time patterns and introduce a concept to analytically predict complex patterns in networks of stuart landau oscillators with linear symmetric and instantaneous coupling based solely on the network topology these patterns consist of partial amplitude death and partial synchronization and are found to exist in large variety for all undirected networks of up to 5 nodes the underlying concept is proved to be robust with respect to frequency mismatch and can also be extended to larger networks in addition it directly links the stability of complete in phase synchronization to only a small subset of topological eigenvalues of a network

determining individual phase response curves from aggregate population data phase reduction is an invaluable technique for investigating the dynamics of nonlinear limit cycle oscillators central to the implementation of phase reduction is the ability to calculate phase response curves prcs which describe an oscillator s response to an external perturbation current experimental techniques for inferring prcs require data from individual oscillators which can be impractical to obtain when the oscillator is part of a much larger population here we present a simple methodology to calculate prcs of individual oscillators using an aggregate signal from a large homogeneous population this methodology is shown to be accurate in the presence of interoscillator coupling and noise and can also provide a good estimate of an average prc of a heterogeneous population we also find that standard experimental techniques for prc measurement can produce misleading results when applied to aggregate population data

chimera states in population dynamics networks with fragmented and hierarchical connectivities we study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a hopf bifurcation this dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions the complexity of the dynamics arises from the presence of a limit cycle and four fixed points when the bifurcation parameter increases away from the hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes followed by long resting periods we observe chimera states in this spiking regime as a coexistence of coherence synchronization and incoherence desynchronization in a one dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters we also show that hierarchical fractal coupling topologies induce traveling multichimera states the speed of motion of the coherent and incoherent parts along the ring is computed through the fourier spectra of the corresponding dynamics

symmetries stability and control in nonlinear systems and networks this paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks specifically it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems this synergy between structural properties symmetries and convergence properties contraction is illustrated in the contexts of network motifs arising for example in genetic networks from invariance to environmental symmetries and from imposing different patterns of synchrony in a network

synchronization of two interacting populations of oscillators we analyze synchronization between two interacting populations of different phase oscillators for the important case of asymmetric coupling functions we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators it includes three types of bistabilities higher order entrainment and the existence of states with unusual stability properties all possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically the impact of these findings for neuroscience is discussed

completely non clausal theorem proving the proof procedure we describe operates on quantifier free formulas of the predicate calculus which are not truth functionally normalized in any way the procedure involves a single inference rule called nc resolution and is shown to be complete completeness is also obtained for a simple restriction on the rule s application examples are given using nc resolution to derive a logic program from its specification and to execute a program specification in its original form

cluster consensus in discrete time networks of multiagents with inter cluster nonidentical inputs in this paper cluster consensus of multiagent systems is studied via inter cluster nonidentical inputs here we consider general graph topologies which might be time varying the cluster consensus is defined by two aspects intracluster synchronization the state at which differences between each pair of agents in the same cluster converge to zero and inter cluster separation the state at which agents in different clusters are separated for intra cluster synchronization the concepts and theories of consensus including the spanning trees scramblingness infinite stochastic matrix product and hajnal inequality are extended as a result it is proved that if the graph has cluster spanning trees and all vertices self linked then the static linear system can realize intra cluster synchronization for the time varying coupling cases it is proved that if there exists t 0 such that the union graph across any t length time interval has cluster spanning trees and all graphs has all vertices self linked then the time varying linear system can also realize intra cluster synchronization under the assumption of common inter cluster influence a sort of inter cluster nonidentical inputs are utilized to realize inter cluster separation such that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs in addition the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory as an application we employ a modified non bayesian social learning model to illustrate the effectiveness of our results

lattice implication ordered semigroups from the viewpoint of semantics lattice implication algebras provide a basis to establish lattice valued logic with truth value in a relatively general lattice in this paper we first introduce two notions of lattice implication n ordered semigroup and lattice implication p ordered semigroup which induced by lattice implication algebras secondly we study some of their basic properties and prove that a lattice implication n ordered semigroup is a residuated semigroup and a lattice implication p ordered semigroup is an arithmetic lattice ordered semigroup we also define the homomorphism mapping between lattice implication n ordered semigroups finally we discuss some properties of filters and sl ideals in lattice implication n ordered semigroups and lattice implication p ordered semigroups

filter based resolution principle for lattice valued propositional logic lp x as one of most powerful approaches in automated reasoning resolution principle has been introduced to non classical logics such as many valued logic however most of the existing works are limited to the chain type truth value fields lattice valued logic is a kind of important non classical logic which can be applied to describe and handle incomparability by the incomparable elements in its truth value field in this paper a filter based resolution principle for the lattice valued propositional logic lp x based on lattice implication algebra is presented where filter of the truth value field being a lattice implication algebra is taken as the criterion for measuring the satisfiability of a lattice valued logical formula the notions and properties of lattice implication algebra filter of lattice implication algebra and the lattice valued propositional logic lp x are given firstly the definitions and structures of two kinds of lattice valued logical formulae i e the simple generalized clauses and complex generalized clauses are presented then finally the filter based resolution principle is given and after that the soundness theorem and weak completeness theorems for the presented approach are proved

fuzzy implicative and boolean filters of r 0 algebras the notions of fuzzy filters fuzzy implicative filters and fuzzy boolean filters are introduced in r0 algebras respectively some of their properties are investigated the relations between fuzzy implicative filters and fuzzy boolean filters are discussed the characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent 1 a fuzzy filter f is implicative 2 f is a fuzzy boolean filter 3 x y z l f x z f x z y f y z 4 x y l f x y f x y y 5 x l n 1 f nx f x

network synchronization of groups in this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups both continuous time and discrete time systems are considered we initially focus on the case where two groups are present and the network has bipartite topology i e links exist between nodes in different groups but not between nodes in the same group we also show that group synchronous motions are compatible with more general network topologies where there are also connections within the groups

perturbation analysis of complete synchronization in networks of phase oscillators the behavior of weakly coupled self sustained oscillators can often be well described by phase equations here we use the paradigm of kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators the topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network laplacian which influence the synchronization frequency in a particular way they characterize the importance of nodes in a network and the relations between them expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale free random networks and for a erdos renyi random network we briefly discuss an application of the perturbation theory in the second order to network structural analysis

existence of hysteresis in the kuramoto model with bimodal frequency distributions we investigate the transition to synchronization in the kuramoto model with bimodal distributions of the natural frequencies previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip here we show that proximity to the unimodal bimodal border does not necessarily imply hysteresis when the width but not the depth of the central dip tends to zero we draw this conclusion from a detailed study of the kuramoto model with a suitable family of bimodal distributions

gaussian noise and the two network frustrated kuramoto model abstract we examine analytically and numerically a variant of the stochastic kuramoto model for phase oscillators coupled on a general network two populations of phased oscillators are considered labelled blue and red each with their respective networks internal and external couplings natural frequencies and frustration parameters in the dynamical interactions of the phases we disentangle the different ways that additive gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a laplacian decomposition for the sub graphs for blue and red under the linearisation ansatz that the oscillators of each respective network remain relatively phase synchronised centroids or clusters we are able to obtain simple closed form expressions using the fokker planck approach for the dynamics of the average angle of the two centroids in some cases this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials these considerations are extended to a regime where one of the populations has fragmented in two the analytic expressions we derive largely predict the dynamics of the non linear system seen in numerical simulation in particular we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented

fixed points and stability in the two network frustrated kuramoto model we examine a modification of the kuramoto model for phase oscillators coupled on a network here two populations of oscillators are considered each with different network topologies internal and cross network couplings and frequencies additionally frustration parameters for the interactions of the cross network phases are introduced this may be regarded as a model of competing populations internal to any one network phase synchronisation is a target state while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor we conduct fixed point analyses for two regimes one where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other the second where one part of a population remains fixed in phase in relation to the other population but where instability may occur within the first population leading to fragmentation we compare analytic results to numerical solutions for the system at various critical thresholds

determination of α resolution in lattice valued first order logic lf x key issues for resolution based automated reasoning in lattice valued first order logic lf x are investigated with truth values in a lattice valued logical algebraic structure lattice implication algebra lia the determination of resolution at a certain truth value level called a resolution in lf x is proved to be equivalently transformed into the determination of a resolution in lattice valued propositional logic lp x based on lia the determination of a resolution of any quasi regular generalized literals and constants under various cases in lp x is further analyzed specified and subsequently verified hence the determination of a resolution in lf x can be accordingly solved to a very broad extent which not only lays a foundation for the practical implementation of automated reasoning algorithms in lf x but also provides a key support for a resolution based automated reasoning approaches and algorithms in lia based linguistic truth valued logics

self emerging and turbulent chimeras in oscillator chains we report on a self emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators this chimera i e a state with coexisting regions of complete and partial synchrony emerges via a supercritical bifurcation from a homogeneous state we develop a theory of chimera based on the ott antonsen equations for the local complex order parameter applying a numerical linear stability analysis we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony

collective phase description of globally coupled excitable elements we develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations collective phase equations describing macroscopic rhythms of the system are derived from langevin type equations of globally coupled active rotators via a nonlinear fokker planck equation the theory is an extension of the conventional phase reduction method for ordinary limit cycles to limit cycle solutions in infinite dimensional dynamical systems such as the time periodic solutions to nonlinear fokker planck equations representing macroscopic rhythms we demonstrate that the type of the collective phase sensitivity function near the onset of collective oscillations crucially depends on the type of the bifurcation namely it is type i for the saddle node bifurcation and type ii for the hopf bifurcation