Abstract
This work presents and investigates a new chaotic system with eight terms. By numerical simulation, the two-scroll chaotic attractor is found for some certain parameters. And, by theoretical analysis, we discuss the dynamical behavior of the new-type Lorenz-like chaotic system. Firstly, the local dynamical properties, such as the distribution and the local stability of all equilibrium points, the local stable and unstable manifolds, and the Hopf bifurcations, are all revealed as the parameters varying in the space of parameters. Secondly, by applying the way of Poincaré compactification inℝ3, the dynamics at infinity are clearly analyzed. Thirdly, combining the dynamics at finity and those at infinity, the global dynamical behaviors are formulated. Especially, we have proved the existence of the infinite heteroclinic orbits. Furthermore, all obtained theoretical results in this paper are further verified by numerical simulations.
Highlights
As a magical and charming nonlinear phenomenon, has attracted attentions of many scholars in nonlinear dynamics community. is is because it is a mysterious and profound subject and because it is beneficial to many practical applications
Some of them were interested in finding different kinds of new chaotic models and discussed their dynamical properties, for example, Lusystem [9], Chen system [10], Lorenz-type system [11,12,13,14], and other new chaotic system [15,16,17,18,19], while some of them focused their attentions on revisiting the existing chaotic system and explored some new phenomena which had not been found before [20,21,22,23,24,25,26,27,28]
By combining theoretical analysis and numerical simulations, we rigorously investigated the dynamics at finity and at infinity of system (5)
Summary
As a magical and charming nonlinear phenomenon, has attracted attentions of many scholars in nonlinear dynamics community. is is because it is a mysterious and profound subject and because it is beneficial to many practical applications. The authors [6] proposed the following new 3D chaotic system with a closed circle of the equilibrium points:. We consider the local dynamical properties for system (5), including the existence and the stability of all equilibrium points, Hopf bifurcation, and the local structure of trajectories. We will discuss the local dynamical properties of equilibrium point E0 in the following three sections. (2) When c − d 0, d > a, and b > 0, the equilibrium point E0 has three eigenvalues λ1 > 0, λ3 < 0, and λ2 0, which means E0 is nonhyperbolic point and is of saddle-center type.
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