Chaotic transition in a five-coupled φ4-field soliton system

Cooperative motions of solitons in a cross-shaped system formed by five chains are numerically studied by solving a set of perturbed φ4-field equations with inter-chain couplings. We find the partially synchronized phase, which exists in a region between the completely synchronized phase and the asynchronized phase. We observe the chaotic transition due to the reconstruction of the synchronized state in the partially synchronized phase, in which the solitons make clusters. We investigate the time-evolution of the number of clusters. The distribution function of the duration time of the state in which all solitons synchronize, namely, when the number of clusters is equal to 1, is expressed as a −32 power law. The power spectrum for the time-variation of the number of clusters also shows a power law. When we examine these calculations in a five-coupled logistic map system, good agreement between the results in these systems can be obtained. The chaotic transition phenomenon presented in a five-coupled oscillator system is closely related to the onset of the on–off intermittency.