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Collective motion of mutually coupled Thomas Oscillators: Spatially Separated 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 in a dynamic environment. We claim our model calculations can explain the diffusion of interacting particles in a fluid. In an ordinary fluid, frequent momentum transfer between particles keeps the particles in a fluid moving together with correlated time behaviour. The diffusion of interacting particles in a dynamic environment like this is a nonequilibrium phenomenon and is similar to the observed transient chaotic dynamics in the model. The detailed study of the nature of dynamics and synchronization reveals that, for two qualitatively different regimes of system parameters, the coupled system passes through an interval of transient chaos before it settles into a chaotic or limit cycle attractor. The linear diffusive coupling is equivalent to weak momentum transfer, leading to conventional dynamics and synchronization. The sinusoidal nonlinear coupling, harmonic momentum transfer, produces exceptional dynamical features. The nature of synchronization is complete(directed motion) when the attractor is chaotic or an unstable transient attractor. 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 a Chiral Phenomenon.