Time-Averaged Behaviour at the Critical Parameter Point of Transition to Spatiotemporal Chaos

A time-averaged behaviour is found to be important for investigating the critical behaviour in parameter space for the transition from temporal chaos to spatiotemporal chaos by using an energy representation. Considering any wave solution as a superposition of the steady wave with its perturbation wave, we find that when approaching to the critical parameter point, their averaged positive interaction energy for the k = 1 mode becomes competitive with the negative one, with the summation displaying a scaling behaviour of power law.