On dynamics analysis of a new chaotic attractor
Introduction
Since Lorenz found the first chaotic attractor in a smooth three-dimensional autonomous system, considerable research interests have been made in searching for the new chaotic attractors. In 1976, Rössler found a three-dimensional autonomous smooth chaotic system. Later, more and more attractors were found. Some new chaotic systems were recently coined, such as Chen system, Lü system, Liu system, the generalized Lorenz system family, and the hyperbolic type of the generalized Lorenz canonical form [1], [2].
A new chaotic system is discussed in this Letter, its coined process is similar to the Lü attractor coined. It is a three-dimensional autonomous system, according to the detailed numerical simulation as well as the theoretical analysis, the chaotic attractor obtained from this new system is also the butterfly-shaped attractor. The chaotic system is a new attractor which is similar to the Lorenz chaotic attractor, but it is not topological equivalent with the Lorenz chaotic system [3], [4]. This Letter is devoted to a more detailed analysis of this new chaotic attractor.
Section snippets
Finding the new chaotic system
In this section, we briefly describe how the anti-control procedure suggested in [4], [5] leads to the finding of the new chaotic attractor.
Start with the controlled Lorenz system [3]: where a, b, c are constants, currently not in the range of chaos, and u is a linear feedback controller in the following form in which , , are constant gains to be determined. The controlled system Jacobian evaluated at is given by
Some basic properties of the new system
In this section, we will investigate some basic properties of the new system (6).
Conclusions
In this Letter, we have constructed a new chaotic system (6). This new chaos attractor is different from the Lorenz attractor. In the new chaotic system, there are abundant and complex dynamical behaviors. The topological structure of the new system should be completely and thoroughly investigated, and the forming mechanism of the system (6) needs further studying and exploring. It is expecting that more detailed theory analyses and simulation investigations will be provided in a forthcoming
Acknowledgement
The authors are grateful to the National Natural Science Foundation of Chain (60503027).
References (8)
- et al.
Chaos Solitons Fractals
(2004) The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors
(1982)Phys. Lett. A
(2008)- et al.
Int. J. Bifur. Chaos
(2002)
Cited by (164)
A Chen-Like Model: High Periodicity Leading to Chaotic Dynamics
2023, International Journal of Bifurcation and ChaosElegant automation: Robotic analysis of chaotic systems
2023, Elegant Automation: Robotic Analysis Of Chaotic SystemsA Lorenz-like Chaotic OTA-C Circuit and Memristive Synchronization
2023, Chaos Theory and ApplicationsDynamic Analysis and Adaptive Synchronization of a New Chaotic System
2023, Journal of Applied Nonlinear DynamicsOn the Dynamics and FSHP Synchronization of a New Chaotic 3-D System with Three Nonlinearities
2023, Nonlinear Dynamics and Systems TheoryBifurcation analysis and chaos control in Zhou's dynamical system
2022, Engineering Computations (Swansea, Wales)