Abstract:
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 rst
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 pro-
le, the existence of several dynamical states together with chimera states is identi ed 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 e ect of ring regularity in the observed states. Interestingly, we
nd that the coherent motion of the neuronal network promotes the entire system to regular ring.
