A chaotic hyperjerk system based on memristive device.

*(English)*Zbl 1354.34092
Vaidyanathan, Sundarapandian (ed.) et al., Advances and applications in chaotic systems. Cham: Springer (ISBN 978-3-319-30278-2/hbk; 978-3-319-30279-9/ebook). Studies in Computational Intelligence 636, 39-58 (2016).

Summary: From the mechanical system point of view, third-order derivatives of displacement or the time rate of change of acceleration is the jerk, while the fourth derivative has been known as a snap. As a result, a dynamical system which is presented by an \(n\)th order ordinary differential equation with \(n>3\) describing the time evolution of a single scalar variable is considered as a hyperjerk system. Hyperjerk system has received significant attention because of its elegant form. Motivated by reported attractive hyperjerk systems, a 4-D novel chaotic hyperjerk system has been introduced and studied in this work. Interestingly, this hyperjerk system displays an infinite number of equilibrium points because of the presence of a memristive device. In addition, an adaptive controller is proposed to achieve synchronization of such novel hyperjerk systems with two unknown parameters. In order to confirm the feasibility of the mathematical hyperjerk model, its electronic circuit is designed and implemented by using SPICE.

For the entire collection see [Zbl 1350.93004].

For the entire collection see [Zbl 1350.93004].

##### MSC:

34D06 | Synchronization of solutions to ordinary differential equations |

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

34C28 | Complex behavior and chaotic systems of ordinary differential equations |

94C05 | Analytic circuit theory |