This model reveals self-oscillation in dynamical systems with strange attractors, indicating chaotic behavior.
We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order integro-differential equation which mimics a spring-like problem. We determine the potential energy, the rate of change of the kinetic energy of this system, and show that is self-oscillating.
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Nicola Romanazzi (2025) studied this question.
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