Extreme Events in a Chaotic Map-Based Higher-Order Neuronal Model

Higher-order networks represent complex multinode interactions beyond what traditional pairwise models can capture, offering deeper insights into many real-world system dynamics. Synchronization of complex networks is essential for achieving coordinated behavior, promoting efficient communication, stability, and overall functionality across various domains, including neuroscience. Extreme events, marked by abrupt and significant deviations from typical behavior that surpass a statistical threshold, can severely affect system stability and performance. Understanding and managing these events are vital for improving resilience and preventing catastrophic failures within complex networks and dynamical systems. This paper explores synchronization and extreme events in the synchronous solutions of a higher-order Chialvo neuron map network model, utilizing inner-linking functions and chemical synapses to represent pairwise and nonpairwise interactions, respectively. By applying Master Stability Functions and assessing synchronization error, we derive synchronization criteria and investigate the potential for extreme events within stable synchronous regions. Our findings indicate that the emergence of extreme events is contingent on the values of the higher-order coupling parameter, while the pairwise coupling parameter is responsible for sustaining synchronization. In response to these events, we develop a control strategy to suppress extreme events and chaotic behavior. Our results demonstrate that connecting all nodes to an external reference source is necessary to stabilize the network and maintain synchronization, as partial control proved insufficient.