On the features of nonlinear analysis of dynamical systems based on the matrix decomposition method

In this paper, we consider the application of the matrix decomposition method to analyze Chua’s chaotic oscillator. It is shown that Chua’s system of equations describing the oscillator can be expanded into linear, quadratic, and cubic terms using the matrix decomposition method. Decomposition into a matrix series permits to study transition to chaos in Chua’s system from the point of view of Landau’s model of initial turbulence. The emerging new chaotic state in the system when a new stationary value of a state-space variable is chosen is explained using the Poincaré section method. For the system of equations that are obtained using the matrix decomposition method, the spectral and bifurcation analysis is conducted. Simulations using MATLAB and Simulink are carried out. A computational Simulink-model is the basis for building an information technology for recognizing the chaotic dynamics of Chua-type oscillators.

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