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 the critical parameter point the 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.
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The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, and Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing 100875 Beijing Radiation Center, Beijing 100875;
