Discrete Memristive Hindmarsh-Rose Neural Model with Fractional-Order Differences

Discrete systems can offer advantages over continuous ones in certain contexts, particularly in terms of simplicity and reduced computational costs, though this may vary depending on the specific application and requirements. Recently, there has been growing interest in using fractional differences to enhance discrete models’ flexibility and incorporate memory effects. This paper examines the dynamics of the discrete memristive Hindmarsh-Rose model by integrating fractional-order differences. Our results highlight the complex dynamics of the fractional-order model, revealing that chaotic firing depends on both the fractional-order and magnetic strength. Notably, certain magnetic strengths induce a transition from periodic firing in the integer-order model to chaotic behavior in the fractional-order model. Additionally, we explore the dynamics of two coupled discrete systems, finding that electrical coupling leads to the synchronization of chaotic dynamics, while chemical coupling ultimately results in a quiescent state.