Can Hamilton energy feedback suppress the chameleon chaotic flow?

Abstract

The dynamical behaviors of nonlinear systems are much dependent on the parameter setting and nonlinear terms, and some controllable parameters can be adjusted to modulate the outputs of dynamical systems. This paper confirms that the dynamical behaviors of the chameleon chaotic flow can be regulated by using the scheme of the Hamilton energy feedback. The Hamilton energy function can be approached by using the Helmholtz’s theorem. The dynamical system is improved by adding one new variable associated with Hamilton energy, and the feedback gain for energy is adjusted to find target orbits. The Lyapunov exponent, which is used to discern the emergence of chaos when positive value is approached, is calculated when energy feedback is applied, and the phase portraits are also plotted to understand the stability of oscillation behaviors. It is found that setting appropriate positive feedback gain for Hamilton energy can suppress the chaos. It could be helpful for further stability control of other complex dynamical systems.