# Stochastic Disruption of Synchronization Patterns in Coupled Non-Identical Neurons
## 5 Conclusions  
In this study, we examined the stochastic disruption of synchronization in a system of two non-identical Rulkov neurons coupled via an electrical synapse. Our analysis uncovered regions of mono-, bi-, and tristability, demonstrating how distinct synchronization regimes arise as a function of coupling strength. Through parametric exploration, we identified conditions under which stochastic perturbations to the coupling parameter induce a transition from lag synchronization to monostable in-phase synchronization. Methodologically, this study combines direct numerical simulations with an analytical framework based on confidence ellipses, providing a powerful tool for identifying and predicting the onset of noise-induced excitations. We extended the confidence domain method, which typically focuses on noise-induced transitions in isolated systems or low-dimensional maps, to a two-parameter space (coupling strength and noise intensity) in a  
Figure 13: Largest Lyapunov exponent \(\Lambda\) of the stochastic system (2) with \(\gamma=-1.75\) and \(\Delta=0.002\). (**a**) \(\Lambda\) as a function of noise intensity \(\varepsilon\) for different values of the coupling strength \(\sigma\). (**b**) Two-parameter diagram of \(\Lambda\) in the \((\sigma,\varepsilon)\)-plane showing zones of regular and chaotic dynamics separated by the bifurcation line \(\Lambda=0\). coupled neural system. This enabled us to map out the boundaries between regimes of regular, intermittent, and chaotic behavior and to link these regions with the geometry of transient basins. These findings advance our understanding of how stochastic effects influence synchronization in coupled neuronal systems and offer valuable insights into noise-driven dynamics in both biological and artificial neural networks. We demonstrate that noise can induce a transition from a multistable asynchronous regime to a monostable synchronous regime in a network of coupled neurons exhibiting regular (non-chaotic) dynamics in the deterministic limit. To our knowledge, this specific type of noise-induced synchronization through monostabilization has not been reported in previous studies. We identify a novel intermittency regime in which synchronous three-cycles are sporadically interrupted by noise-driven, asynchronous chaotic bursts. This behavior reflects transitions between metastable states and is governed by the underlying structure of chaotic transient basins, a mechanism not previously emphasized in the context of Rulkov models or in the broader literature on stochastic synchronization. A central finding of this work is the noise-induced intermittency within the synchronous three-cycle regime, where increasing noise intensity leads to transient episodes of desynchronization characterized by chaotic bursts. We showed that this behavior is closely linked to the presence of chaotic transient basins, which act as precursors to the disruption of stable synchronization. Moreover, we identified a specific range of noise intensities where this intermittency persists, with its statistical properties such as laminar phase duration being highly sensitive to the coupling strength. This intermittency differs from previously reported cases in two important ways: (i) it does not follow universal scaling laws, with the scaling behavior varying depending on the coupling strength and noise intensity; and (ii) counterintuitively, weak noise can stabilize laminar dynamics when coupling is strong, resulting in an increased probability of synchronized behavior with increasing noise. These features are closely linked to the presence of chaotic transient basins in the system state space. Future directions include extending this framework to larger and more complex networks, exploring the role of network topology, and investigating practical implications for neuromorphic engineering and biomedical modeling of brain activity under noisy conditions.