Symmetry breaking phenomena in a network of nonlocally coupled tristable 2D Tagne Nkounga–Yamapi neuronal models

This paper is based on the collective dynamics of a coupled neural network, each node of which is modelled using the extended FitzHugh–Nagumo model, called for instance the Tagne Nkounga–Yamapi neuronal model, whose main property is the coexistence of three stable attractors: (i.e.) a tristable system with two oscillating attractors and one stationary attractor. Depending mainly on the coupling parameter, this study highlights the presence of several states, including incoherence, coherence, the phenomenon of symmetry breaking, also known as chimera states, and solitary states. It is important to note that coupling parameter causes oscillations to be created in the initially stationary attractor. Subsequently, in this work, for some fixed values of coupling parameter, we obtain a chimera state characterised by the presence of a combination of incoherence, coherence, and solitary states with the property of having a few solitary oscillators escaping from a completely coherent group, appearing in a disordered manner in space. An interesting phenomenon is the ability of coupling to force some oscillators to change their original attractor. In other words, when the coupled oscillators are all initially in the same attractor, increasing the coupling forces the oscillators to gradually change attractors. The transition between one attractor to another one nd the reverse transition. This makes it possible to highlight more precise values of coupling in the tristable model of the multi-solitary chimera state with three attractors, characterised by the presence of several solitary states located in two different attractors against a background of a chimera state with a single attractor. It should also be noted that the initial conditions play an important role in that it will be impossible to obtain some states (notably multi-solitary chimera states) if the initial values of the oscillators are not taken around a particular attractor.