On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type

Abstract

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.

Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example

“…An example of the circuitry realization of the Lorenz system is provided as well, although unfortunately without experimental verification. Paper [170] can be understood as a direct extension of the above-mentioned ideas. An approach known as the firmly grounded backward-forward integration method has been algorithmized, and was applied to the construction of a high-precision approximate solution of the chaotic dynamics, namely piecewise smooth chaotic systems having quadratic nonlinearity or systems with hysteresis.…”