Darboux integrability of a hyperjerk memristive system

Abstract

In this work, we investigate the following novel four-dimensional dynamical memristive system (see, (Prousalis et al., 2017)) This system, in a certain area of the parameter space, exhibits hyper-jerk dynamics and a line of singularities passing through the origin, It may be regarded as a dynamical system including hidden attractors. The behavior of the proposed system is studied through polynomial first integrals and a Darboux first integral. We first prove that the system has a minimal polynomial first integral. In addition, all the invariant algebraic surfaces and exponential factors of this suggested system are computed. Then, we prove that this type of system doesn’t have a first integral of the Darboux type.

Keywords

• chaos system
• darboux first integrals
• limit cycle.