Wave patterns formation in one-dimensional networks of coupled neuron-like oscillators

Dynamics of two types of one-dimensional networks of electrically coupled neuron-like oscillators implemented using analog electronic circuits are investigated. The networks mimic interacting excitable or bistable neurons which are coupled via gap junctions. The first network is composed of FitzHugh-Nagumo oscillators and the second one is composed of modified FitzHugh-Nagumo oscillators with additional conductance. It is forecasted theoretically and shown experimentally that in both types of networks there exist a variety of different propagating waves: fonts (kink and antikink), excitation pulses, periodic waves and solitary bound states. The fronts and pulses can annihilate or demonstrate particles-like behavior during the interaction with each other and borders of networks. It is shown that particle-like behavior can lead to formation of complex periodic spatiotemporal wave patterns. Besides the periodic patterns in modified FitzHugh-Nagumo network there exist chaotic fractal-like spatiotemporal patterns. It is demonstrated theoretically that emergence of complex patterns can be associated with the existence of a heteroclinic and/or gomoclinic contours in the phase space of corresponding traveling wave systems.