Collective Motion Of Mutually Coupled Thomas Oscillators: Spatially Seperated Swirling Motion And Eddy Diffusion

In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling. Thomas system is a biologically motivated system with feedback circuits and extraordinary dynamical features that can lead to the design of novel materials. Our model calculations can explain the diffusion of interacting particles in a fluid for the specific choice of system parameters. In a fluid, frequent momentum transfer between particles keeps them moving with correlated time behaviour, and we treat it as a synchronization process. The linear diffusive coupling is equivalent to weak momentum transfer, leading to conventional dynamics and synchronization. The sinusoidal nonlinear coupling, or harmonic momentum transfer, produces exceptional dynamical features. The coupled system passes through an interval of transient chaos before it settles into a chaotic or limit cycle attractor. When the attractor is chaotic or an unstable transient attractor, the nature of synchronization is complete (directed motion). In contrast, it is either lag, anti-lag, or space lag for a limit cycle. In such situations, the diffusion is due to particles pedalling and eddy/swirling motion on top of translatory motion via transient chaos. Also, the trajectories of the two particles in the state space resemble the chiral phenomenon.