Applied Mathematics & Information Sciences

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In this paper, a novel three-dimensional (3D) autonomous chaotic system is investigated, which displays complicated dynamical behaviors. Basic dynamical properties are analyzed by means of phase portraits and equilibria. Also, an optimal control law is designed for the novel chaotic system, based on the Pontryagin minimum principle (PMP). Furthermore, an adaptive and feedback control law is introduced to stabilize the new chaotic system with unknown parameters. The adaptive control results are established using the Lyapunov stability theory. Numerical simulations are included to demonstrate the efficiency and high accuracy of the proposed method.