Asymmetric coupling of nonchaotic Rulkov neurons: Fractal attractors, quasimultistability, and final state sensitivity

Abstract: Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron systems. In this paper, we investigate the geometrical properties of the strange attractors, four-dimensional basins, and fractal basin boundaries of an asymmetrically electrically coupled system of two identical nonchaotic Rulkov neurons. We discover a quasimultistability in the system emerging from the existence of a chaotic spiking-bursting pseudo-attractor, and we classify and quantify the system's basins of attraction, which are found to have complex fractal geometries. Using the method of uncertainty exponents, we also find that the system exhibits extreme final state sensitivity, which results in a dynamical uncertainty that could have important applications in neurobiology.