Kerr oscillators parameters

Let us now consider the behavior of the system when the Kerr coupling constant is switched on (e12 / 0). For brevity and clarity, we restrict our discussion to the question of how the attractors in Fig. 20 change when both oscillators interact with each other. To answer this question, let us have a look at the joint auto-nomized spectrum of Lyapunov exponents for the two oscillators A,j, A,2, L3, A-4, L5 versus the interaction parameter 0 < ( 2 < 0.7. The spectrum is seen in Fig. 32 and describes the dynamical properties of our oscillators in a global sense. The dynamics of individual oscillators can be glimpsed at the appropriate phase portraits. Let us now fix our attention on a detailed analysis of Fig. 32. For the limit value ei2 = 0, the dynamics of the uncoupled oscillators has already been presented in Fig. 20. In the case of very weak interaction 0 < C 2 < 0.0005, the system of coupled oscillators manifests chaotic behavior. For C 2 = 0.0005 we obtain the spectrum 0.06,0.00, —0.21, 0.54, 0.89. It is interesting to... 

The emergence of order and chaos in the system of two oscillators depends on the value of the Kerr coupling constant 2- F°r the fixed parameters of damping... 

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