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A complex spatiotemporal pattern with coexisting coherent and incoherent domains in a network of identically coupled oscillators is known as a chimera state. Here, we report the emergence and existence of a novel type of nonstationary chimera pattern in a network of identically coupled Hindmarsh–Rose neuronal oscillators in the presence of synaptic couplings. The development of brain function is mainly dependent on the interneuronal communications via bidirectional electrical gap junctions and unidirectional chemical synapses. In our study, we first consider a network of nonlocally coupled neurons where the interactions occur through chemical synapses. We uncover a new type of spatiotemporal pattern, which we call “spike chimera” induced by the desynchronized spikes of the coupled neurons with the coherent quiescent state. Thereafter, imperfect traveling chimera states emerge in a neuronal hypernetwork (which is characterized by the simultaneous presence of electrical and chemical synapses). Using suitable characterizations, such as local order parameter, strength of incoherence, and velocity profile, the existence of several dynamical states together with chimera states is identified in a wide range of parameter space. We also investigate the robustness of these nonstationary chimera states together with incoherent, coherent, and resting states with respect to initial conditions by using the basin stability measurement. Finally, we extend our study for the effect of firing regularity in the observed states. Interestingly, we find that the coherent motion of the neuronal network promotes the entire system to regular firing.
Several cognitive neuronal processes strictly depend on interneuronal communications that take place mainly through two types of synapses: the electrical communication via gap junctional and the chemical synaptic interaction. Neuronal synchrony plays a fundamental role in the normal operation of various neuronal processes. In particular, this property is closely related to the neuronal plasticity, information exchange, etc. Chimera state is a self-organized complex spatiotemporal pattern that deals with the simultaneous appearance of synchrony and desynchrony behaviors in the neuronal networks. The emergence of the chimera states in the neuronal network was investigated previously by considering the electrical and the chemical synaptic coupling or the interaction through another medium. In all previous studies on chimera states, only bidirectional chemical synaptic interactions were considered. However, in the real situation, chemical communication happens unidirectionally between two neurons, whereas electrical communication happens bidirectionally between two adjacent neurons. In this context, here, we study the existence and emergence of chimera patterns in a neuronal hypernetwork by taking a unidirectional chemical synapse and bidirectional electrical coupling. In our study, each neuron in the network is modeled with a Hindmarsh–Rose neuronal oscillator. Through the interplay of the network topology and the chemical synaptic coupling function, a novel type of nonstationary chimera pattern, called “spike chimera,” is found, which is characterized by uncorrelated spikes and a coherent quiescent state of the coupled neurons. These complex spatiotemporal patterns are robust with respect to initial conditions. We investigate the firing regularities of the coupled neurons in different dynamical states. With the help of various measurements, the different collective dynamical features, such as incoherent, coherent, steady state dynamics, and spike chimera states, are characterized and quantified in the parameter space.
