Chaotic dynamics and fractal geometry in ring lattice systems of nonchaotic Rulkov neurons

Abstract: This paper investigates the complex dynamics and fractal attractors that emerge from a 60-dimensional ring lattice system of electrically coupled nonchaotic Rulkov neurons. Although networks of chaotic Rulkov neurons are well studied, systems of nonchaotic Rulkov neurons have not been extensively explored due to the piecewise complexity of the nonchaotic Rulkov map. We find rich dynamics emerge from the electrical coupling of regular spiking Rulkov neurons, including chaotic spiking, synchronized chaotic bursting, and complete chaos. By varying the electrical coupling strength between the neurons, we also discover general trends in the maximal Lyapunov exponent across different regimes of the ring lattice system. By means of the Kaplan-Yorke conjecture, we also examine the fractal geometry of the ring system's high-dimensional chaotic attractors and find various correlations and differences between the fractal dimensions of the attractors and the chaotic dynamics on them.