# Stochastic Disruption of Synchronization Patterns in Coupled Non-Identical Neurons
###### Abstract  
We investigate the stochastic disruption of synchronization patterns in a system of two non-identical Rulkov neurons coupled via an electrical synapse. By analyzing the system deterministic dynamics, we identify regions of mono-, bi-, and tristability, corresponding to distinct synchronization regimes as a function of coupling strength. Introducing stochastic perturbations to the coupling parameter, we explore how noise influences synchronization patterns, leading to transitions between different regimes. Notably, we find that increasing noise intensity disrupts lag synchronization, resulting in intermittent switching between a synchronous three-cycle regime and asynchronous chaotic states. This intermittency is closely linked to the structure of chaotic transient basins, and we determine a noise intensity range in which such behavior persists, depending on the coupling strength. Using both numerical simulations and an analytical confidence ellipse method, we provide a comprehensive characterization of these noise-induced effects. Our findings contribute to the understanding of stochastic synchronization phenomena in coupled neuronal systems and offer potential implications for neural dynamics in biological and artificial networks. R 2025 13 May 2025 27 May 20  
Both deterministic and stochastic behaviors in isolated Rulkov neurons have been the focus of extensive research [23; 24; 25; 26; 27]. The Rulkov map strikes a compelling balance between biological realism and mathematical simplicity, distinguishing it from other discrete-time dynamical systems. Its ability to replicate key neuronal behaviors, such as spiking, bursting, and excitability, within a low-dimensional, discrete-time framework has made it a popular choice in computational neuroscience. This efficiency makes it especially suitable for large-scale simulations of neuronal networks, where computational resources are a limiting factor. Additionally, its structural simplicity allows for in-depth analytical exploration of complex dynamical phenomena, including bifurcations, chaos, multistability, and noise-induced intermittency. These features make the Rulkov map an invaluable tool for both theoretical studies in nonlinear dynamics and practical modeling of large neuronal systems. Coupled Rulkov neurons exhibit rich dynamical behaviors, including multiple synchronization regimes that depend on the coupling strength and system parameters [28; 29; 30]. Depending on the coupling parameter, different dynamical regimes (mono-, bi-, and tristable) and synchronous states, such as in-phase and lag synchronization, can emerge. While previous studies have focused primarily on noise-induced effects in networks of chaotic neurons exhibiting bursting dynamics, our work, to the best of our knowledge, is the first to investigate the impact of stochastic perturbations in a system of coupled regular, non-chaotic neurons that display stable three-cycles in the isolated state. This allows us to explore a previously underexamined regime where noise induces transitions from multistable lag synchronization to monostable in-phase synchronization, as well as intermittent desynchronization via noise-driven chaotic bursts. Through systematic parametric analysis, we identify key conditions under which noise intensity influences the transitions between different dynamical states. To analyze these complex dynamics, we employ a combination of direct numerical simulations and an analytical method based on confidence domains, which provide a robust statistical tool for assessing the variability of system trajectories under stochastic perturbations, allowing us to characterize the range of noise intensity that sustains intermittency and determine its dependence on coupling strength. The size and shape of the confidence domains are determined from the stochastic sensitivity matrices of the corresponding deterministic attractors.