Collective dynamics of a Josephson junction and memristor synapse-coupled Hindmarsh-Rose neurons

Magnetic flux and Josephson junctions play intriguing roles in manifesting the dynamics of biological neurons. To comprehend their importance, we consider a pair of coupled 2D Hindmarsh-Rose (HR) neurons. We begin by investigating the dynamical behavior of diffusively coupled neurons and discover the existence of chaos within a limited range of coupling coefficients. Furthermore, the incorporation of Josephson junctions into the system is found to enhance the complexity of the system dynamics, including the possibility of hyper-chaotic behavior, which depends on the junction coefficient and coupling strength. Additionally, we investigate the impact of memristor synapse coupling in HR neurons both in the presence and absence of Josephson junctions. Our findings indicate that complex behaviors are more pronounced when Josephson junctions are present compared to their absence. In addition, we look into the associated dynamics of a collection of neurons with Josephson junctions, which leads to a transition to a coherent oscillatory state. Furthermore, the flux-coupled HR neurons with Josephson junctions lead to a resting state in the neurons. These observations provide clear evidence that coupled neurons via Josephson junctions enable the manifestation of rich, complex dynamics, while the interplay of magnetic flux with Josephson junctions influences the system toward coherent oscillations or quiescence.