Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

<span>This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM results</span>

Bifurcation Analysis and Electronic Circuit for Sprott Jerk System

In this paper, the Sprott jerk system based quadratic function is presented. The dynamics of this system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. The Sprott system can exhibit a chaotic attractor, which has complex dynamic behavior. Finally, the circuit implementation is carried out to verify the Sprott Jerk system. The comparison between the MATLAB and MultiSIM simulation results demonstrate the effectiveness of the Sprott system.

A Novel Nonideal Flux-Controlled Memristor Model for Generating Arbitrary Multi-Double-Scroll and Multi-Double-Wing Attractors

This paper proposes a novel nonideal flux-controlled memristor model with a multipiecewise linear memductance function, which can be used to construct a memristive multi-scroll or multi-wing chaotic system. Importantly, arbitrary multi-double-scroll and multi-double-wing attractors can be generated depending on this memristor model directly and without the need to change the original nonlinear terms of the system. Another highlight is that the odd or even number of the double-scroll and double-wing attractors can also be freely controlled by the memristor model. To further illustrate these unique features, by introducing the memristor model into two classical chaotic systems, i.e. Jerk system and Lorenz system, multi-double-scroll and multi-double-wing chaotic attractors are obtained respectively. The formation mechanism of the multi-double-wing and multi-double-scroll attractors is also discussed. Moreover, the randomness of the chaotic binary sequences generated by the proposed memristor model is tested by the National Institute of Standards and Technology test suite. The tested results are better than those of the well-known Lorenz system. Furthermore, the corresponding circuits are constructed. The experimental results and the numerical simulations coincide well with each other, showing the effectiveness and feasibility of the proposed memristor model.