Multistable dynamics and control of a new 4D memristive chaotic Sprott B system

This work proposes and investigates the dynamic behavior of a new memristive chaotic Sprott B system. One of the interesting features of this system is that it has a bias term that can adjust the symmetry of the proposed model, inducing both homogeneous and heterogeneous behaviors. Indeed, the introduced memristive system can turn from rotational symmetry (RS) to rotational symmetry broken (RSB) system in the presence or the absence of this bias term. In the RS system (i.e., absence of the bias term), pairs of symmetric attractors are formed, and the scenario of attractor merging is observed. Coexisting symmetric attractors and bifurcations with up to four solutions are perfectly investigated. In the RSB system (i.e., the bias term is non-zero), many interesting phenomena are demonstrated, including asymmetric attractors, coexisting asymmetric bifurcations, various types of coexisting asymmetric solutions, and period-doubling transition to chaos. We perfectly demonstrate that the new asymmetric/symmetric memristive system exhibits the exciting phenomenon of partial amplitude control (PAC) and offset boosting. Also, we show how it is possible to control the amplitude and the offset of the chaotic signals generated for some technological exploitation. Finally, coexisting solutions (i.e., multistability) found in the novel memristive system are further controlled based on a linear augmentation (LA) scheme. Our numerical findings demonstrated the effectiveness of the control technic through interior crisis, reverse period-doubling scenario, and symmetry restoring crisis. The coupled memristive system remains stable with its unique survived periodic attractor for higher values of the coupling strength

A New Class of Two-dimensional Chaotic Maps with Closed Curve Fixed Points

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this recordThis paper constructs a new class of two-dimensional maps with closed curve fixed points. Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper parameters of the nonlinear function. The stabilities of these fixed points are studied to show that these fixed points are all non-hyperbolic. Then a computer search program is employed to explore the chaotic attractors in these maps, and several simple maps whose fixed points form different shapes of closed curves are presented. Complex dynamical behaviours of these maps are investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangsu Province of China5th 333 High-level Personnel Training Project of Jiangsu Province of ChinaExcellent Scientific and Technological Innovation Team of Jiangsu UniversityJiangsu Key Laboratory for Big Data of Psychology and Cognitive Scienc