Study of reduced Chialvo map with electromagnetic flux: Dynamics and network behavior

Abstract

We introduce a novel two-dimensional discrete neuron map, which is obtained by adding an electromagnetic flux on a reduced Chialvo map and study various dynamical aspects of the proposed map. We discuss the stability of fixed points, bistability, different bifurcations, S-shape chaotic attractors, and firing patterns. In our exploration, the bistability phenomena showcase the coexistence of different periodic attractors along with the basin of attraction region. We observe that the system undergoes chaotic behavior via period-doubling and reverse period-doubling and also illustrate the behavior of the chaotic bubbles. Further, we explore the numerical continuation of bifurcation for codimension-one and codimension-two of the map. The evolution of chaotic attractor through various states and its associated correlation dimension shows the intricate structure and complexity of the map. Additionally, we extend the dynamical study to the network of neurons, specifically focusing on the ring-star network. This broader investigation shows different dynamic states in the network, like synchronized, unsynchronized, and chimera states. Finally, we vary the coupling strength parameters of the network map and observe that it shows diverse wavy patterns and clustered states.