The aim of this paper is to study the chaos, optimal control, and adaptive control of the hyperchaotic Chen system. In this paper, applying the Pontryagin’s minimum principle (PMP), the optimal control inputs for the interested model are obtained with respect to the selected measure. A piecewise-spectral homotopy analysis method (PSHAM) is used for solving the hyperchaotic Chen system and the extreme conditions obtained from the PMP. Furthermore, an adaptive control approach and a parameter estimation update law are introduced for the hyperchaotic Chen system with completely unknown parameters. The control results are established using the Krasovskii–LaSalle principle. Finally, numerical simulations are included to demonstrate the effectiveness of the proposed control strategy.

Hyperchaos control of the hyperchaotic Chen system by optimal control design

Further study on finite-time synchronization for delayed inertial neural networks via inequality skills

Color image encryption scheme using coupled hyper chaotic system with multiple impulse injections

Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function

In this paper, a quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections is proposed. Firstly, in order to enhance the complexity of trajectory, three impulse signals values are injected into coupled hyper-chaotic Lorenz system during iterations. Then, six sequences generated from this system are used to encrypt red, green and blue components of the quantum color original image by XOR operations and right cyclic shift operations. Six initial values and three impulse signals values are used as keys, which could reduce the burden of keys transmission and make the cryptosystem own a key space large enough to resist exhaustive attack, even the attack from a quantum computer. Numerical simulations demonstrate that the proposed encryption scheme has a good feasibility and effectiveness for protecting quantum color images and is more secure in comparison with other encryption algorithms.

A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections

In this paper, a new three-dimensional autonomous chaotic system is presented. There are three control parameters and three different nonlinear terms in the governed equations. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation. The nonlinear characteristic of the new three-dimensional autonomous system versus the control parameters is illustrated by bifurcation diagram, Lyapunov-exponent spectrum, phase portraits, etc.

Analysis of a new three-dimensional chaotic system

The global asymptotic stability for neutral-type inertial BAM neural networks with time-varying delays is considered. By using variable transforming, homeomorphism theory, suitable Lyapunov functional together with matrix equations, some delay-dependent sufficient conditions are established to ascertain the existence and global asymptotic stability of this neutral-type inertial BAM neural networks. All the conditions are obtained relying on linear matrix inequalities. Finally, two numerical examples are presented to illustrate the validity of theoretical results.

Stability analysis for neutral-type inertial BAM neural networks with time-varying delays

In this paper, a new three-dimensional autonomous chaotic system is presented. There are three control parameters and three different nonlinear terms in the governed equations. The new chaotic system has six equilibrium points. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation. The nonlinear characteristic of the new chaotic system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, a dissipative system, Poincare maps and bifurcations. Then, an adaptive control law is derived to make the states of two identical chaotic systems asymptotically synchronized based on the Lyapunov stability theory. Finally, a numerical simulation is presented to verify the effectiveness of the proposed synchronization scheme.

Hongxing Yao

Papers

Analysis of a new three-dimensional chaotic system

Stability analysis for neutral-type inertial BAM neural networks with time-varying delays

Analysis and adaptive synchronization for a new chaotic system