Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps

We study numerically the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems, which exhibit solitary states along the transition from coherence to incoherence. These partial synchronization patterns are described as states when single or several elements demonstrate different dynamics compared with the behavior of other elements in a network. Using as an example a ring network of nonlocally coupled Lozi maps, we explore the robustness of solitary states to heterogeneity in parameters of local dynamics or coupling strength. It is found that if these network parameters are continuously modulated by noise, solitary states are suppressed as the noise intensity increases. However, these states may persist in the case of static randomly distributed system parameters for a wide range of the distribution width. Domains of solitary state existence are constructed in the parameter plane of coupling strength and noise intensity using a cross-correlation coefficient.

Automated summary

In this study, we numerically investigate the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems. We explore the robustness of solitary states, which occur during the transition from coherence to incoherence, to heterogeneity in local dynamics or coupling strength. The results show that solitary states are suppressed when network parameters are modulated by noise, but they can persist in the case of static randomly distributed system parameters.