Synchronization transition in networks of Fractional-Order memristive Hindmarsh-Rose neurons

Abstract

Fractional-order neurons, which model memory effects in neural systems, are increasingly recognized for their importance in understanding complex neuronal dynamics. Despite extensive research on synchronization in networks of fractional-order neurons, the transition to synchronization in these networks, especially under electromagnetic radiation’s impact on neuron membranes, has been largely overlooked. This study addresses this gap by investigating synchronization transitions in small-world and scale-free networks composed of fractional-order and integer-order memristive Hindmarsh-Rose neurons. The results reveal that fractional-order neurons synchronize at smaller coupling strengths than integer-order neurons and exhibit more abrupt synchronization transitions, particularly in scale-free networks with dense connections. These findings underscore the critical role of memory effects and network topology in the emergence of synchronization behavior in neuronal networks.