Modeling for Spatio-Temporal Chaos

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To understand spatio-temporal chaos better, we have studied simple model eqations. The creation and annihilation processes of characteristics spatial structures is typical of the spatio-temporal chaos. The reconnection of roll structures is a fundamental process in defect chaos.We have studied the Burgers equation with an additional instability term. A characteristic spatial structure in this system is the shock structure. In the spatio-temporal chaos, there appear many shocks and they collide with each other. Two shocks are merged into one shock as a resut of the collision. A new shock is spontaneously created in a long interval between two neighboring shocks. These creation and merging processes are characteristic of the spatio-temporal chaos in this model equation. We have constructed a simple model for the positions of the shocks and obtained a similar chaotic time evolution including the creation and merging of shocks.We have studied a coupled Ginzburg-Landau equation for another example and found a pulse solution as an attractor. The pulse solution can exhibit breathing motion and splitting bifurcation.As a result, spatio-temporal chaos appears spontaneously from a single pulse solution.