Pattern in nonlinearly coupled network of identical Thomas oscillators

Complexity frontier deals with the study of collective phenomena where one is interested in understanding overwhelmingly intriguing emergent behaviors which comes out as a fact of complex interactions of large number of interacting parts. Spatio-temporal pattern formation which is the emergence of patterns of large-scale behavior is one such fascinating phenomena in complexity science. Emergent phenomena of this sort shed light on to a wide range of collective phenomena and also to its better understanding. One such phenomenon of recent interest is that of chimera states in an ensemble of coupled oscillators. It is the coexistence of coherent and incoherent patterns emerging out on otherwise identical settings of oscillators and coupling topology. This new dynamic state emerges out because of a spontaneous symmetry breaking. Signatures of spatio-temporal evolution in a system of coupled nonlinear oscillators were found and was named domain We have investigated synchronized patterns in a network of Thomas oscillators coupled with sinusoidal nonlinear and linear couplings. Patterns like chimera and cluster states are not only observed for many nonlocally coupled oscillators, it is also observed for nearly local coupled network topology in the case of nonlinear coupling. As coupling radius in-creases, the critical coupling constant for complete synchronization decreases. Crater-like structure is also observed in the snapshot in the case of nonlinear coupling only which agrees with similar observation found in the study of active Brownian particles using the stochastic method. The critical number of oscillators for the onset of chimera is forty and the infinite limit is found to be hundred. No chimera is observed in the zero friction limit due to hyperchaotic motion with large amplitude oscillations, but there is a sharp transi-tion from disorder to order distribution. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

Complexity frontier focuses on the study of collective phenomena arising from complex interactions of a large number of parts, including the formation of spatio-temporal patterns and chimera states. These phenomena shed light on a wide range of collective behaviors and help us better understand complex emergent behaviors.