Neuronal chimera: investigation of spontaneous symmetry breaking in biological oscillator populations

Chimera states are symmetry breaking complex spatiotemporal patterns that emerge as coexistence of both coherent sychronized and incoherent desychronized groups of coupled dynamical systems. Here, we investigate the emergence of chimera states in nonlocal networks of type I Morris–Lecar neurons coupled via chemical synapses. This constitutes a more realistic neuronal modeling framework than previous studies of chimera states, since the Morris–Lecar model provides biophysically more relevant control parameters to describe the activity in actual neural systems. We explore systematically the transitions of dynamic behavior and find that different types of synchrony as well as chimera states appear depending on the excitability level and nonlocal network features. Furthermore, we map the transitions between incoherent states, traveling waves, chimeras, coherent states, and global amplitude death in the parameter space of interest. The obtained results have showed that, besides randomness in initial conditions, the relatively low excitability of the neurons in the oscillatory regime and a moderately high network interaction density are needed for the emergence of chimera states. It is understood that this is also a key condition for rich diversity of dynamical behavior. In addition, interesting multichimera states are observed in the chimera behavior at the boundary of the synchronization region in the parameter space of interest. Neurons that provide synchronization balance in the brain, such as dopamine neurons, can exhibit type I excitability, and it is vital to maintain factors such as level of excitability, balanced excitation activation to prevent this balance from deteriorating. For this reason, it is thought that this thesis has made an important contribution to a better understanding of the biological conditions giving rise to the emergence of chimera states in neural medium. Here we also study the emergence of chimera states, in a population of Morris–Lecar neurons which are coupled by both electrical and chemical synapses, constituting a hybrid synaptic architecture, as in actual brain connectivity. We demonstrate that peculiar dynamical behaviors, including chimera and traveling waves, exist in such a hybrid coupled neural system. We then analyze how the relative abundance of chemical and electrical synapses affects the features of chimera and different synchrony states (i.e. incoherent, traveling wave and coherent). Additionally, we show that, when the relative population of chemical synapses increases further, a new intriguing chaotic dynamical behavior appears above the region for chimera states. This is characterized by the coexistence of two distinct synchronized states with different amplitude, and an unsynchronized state, that we denote as a chaotic amplitude chimera.