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In this letter, we report a numerical study on the collective dynamics of twomutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamicenvironment. We claim our model calculations can explain the diffusion ofinteracting particles in a fluid. In an ordinary fluid, frequent momentumtransfer between particles keeps the particles in a fluid moving together withcorrelated time behaviour. The diffusion of interacting particles in a dynamicenvironment like this is a nonequilibrium phenomenon and is similar to theobserved transient chaotic dynamics in the model. The detailed study of thenature of dynamics and synchronization reveals that, for two qualitativelydifferent regimes of system parameters, the coupled system passes through aninterval of transient chaos before it settles into a chaotic or limit cycleattractor. The linear diffusive coupling is equivalent to weak momentumtransfer, leading to conventional dynamics and synchronization. The sinusoidalnonlinear coupling, harmonic momentum transfer, produces exceptional dynamicalfeatures. The nature of synchronization is complete(directed motion) when theattractor is chaotic or an unstable transient attractor. In contrast, it iseither lag, anti-lag, or space lag for a limit cycle. In such situations, thediffusion is due to particles pedalling and eddy/swirling motion on top oftranslatory motion via transient chaos. Also, the trajectories of the twoparticles in the state space resemble a Chiral Phenomenon.

Collective motion of mutually coupled Thomas Oscillators: Spatially Separated Swirling Motion and Eddy Diffusion