A spectral analysis of chaotic oscillations in simulation model of Chua’s circuit developed with use of matrix decomposition

The A. M. Krot’s matrix decomposition method developed for analysis of complex nonlinear dynamical system attractors based on matrix series in the state space has been used for nonlinear analysis of Chua’s circuit with cube non-linearity. It is shown that the operator of the system of Chua’s differential equations can be represented through the linear, quadratic and cubic terms of the matrix series. The obtained terms are the basis of the simulation model used for carrying out computational experiments. Using the results of the experiments, the values of the control parameters, leading to the chaotic regime, are determined, as well as bifurcation and spectral analysis of the generated signals are carried out. It allows to prove the transition to chaos through a series of bifurcations. The research allowed to draw a conclusion that the process of occurrence of chaotic oscillations in the Chua’s circuit corresponds to the L. D. Landau’s model of initial turbulence in full accordance with the theory of Ruelle – Takens. The correctness of application of the matrix expansion of a vector function depending on values of the perturbations (increments) of variables in the state space is investigated.

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