Abstract
A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.
Highlights
Since Lorenz found the deterministic ordinary nonlinear differential equations has the characteristic of chaotic dynamics [1], chaotic system became a research focus around the world, and many researchers have been proposed many new three-dimensional chaotic systems, such as Chen system [2], Liu system [3], Lü system [4], Bao system [5], Rössler system [6], Sprott system [7], Liu-Chen system [8], Tigan system [9], Zhou system [10], Pham system [11]
With the deep research of chaos system, chaos system is widely used in engineering field
As an important method for secure communication, chaos synchronization is studied by many researchers [16,18,27]
Summary
Since Lorenz found the deterministic ordinary nonlinear differential equations has the characteristic of chaotic dynamics [1], chaotic system became a research focus around the world, and many researchers have been proposed many new three-dimensional chaotic systems, such as Chen system [2], Liu system [3], Lü system [4], Bao system [5], Rössler system [6], Sprott system [7], Liu-Chen system [8], Tigan system [9], Zhou system [10], Pham system [11]. Yalçin [45] designed a multi-scroll chaotic system in a Jerk circuit by using a sine function. Ma et al [47] proposed a multi-scroll chaotic system with a sine function and a feedback controlling function. A sine function input is used in a hyper chaotic Liu system [51] Motivated by these works, we proposed a multi-scroll chaotic system with a special form of a sine function (SFSF), the dynamical properties of this system are analyzed via Lyapunov exponents spectrum, chaotic phase portrait, and bifurcation diagram.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
