Abstract:
The coexistence of coherent and incoherent domains, namely the appearance of chimera states, has been
studied extensively in many contexts of science and technology since the past decade, though the previous studies
are mostly built on the framework of one-dimensional and two-dimensional interaction topologies. Recently, the
emergence of such fascinating phenomena has been studied in a three-dimensional (3D) grid formation while
considering only the nonlocal interaction. Here we study the emergence and existence of chimera patterns in
a three-dimensional network of coupled Stuart-Landau limit-cycle oscillators and Hindmarsh-Rose neuronal
oscillators with local (nearest-neighbor) interaction topology. The emergence of different types of spatiotemporal
chimera patterns is investigated by taking two distinct nonlinear interaction functions. We provide appropriate
analytical explanations in the 3D grid of the network formation and the corresponding numerical justifications are
given. We extend our analysis on the basis of the Ott-Antonsen reduction approach in the case of Stuart-Landau
oscillators containing infinite numbers of oscillators. Particularly, in the Hindmarsh-Rose neuronal network the
existence of nonstationary chimera states is characterized by an instantaneous strength of incoherence and an
instantaneous local order parameter. Besides, the condition for achieving exact neuronal synchrony is obtained
analytically through a linear stability analysis. The different types of collective dynamics together with chimera
states are mapped over a wide range of various parameter spaces.
