Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams
In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2408460 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566446681489408 |
|---|---|
| author | Lilian Huang Wenju Yao Jianhong Xiang Zefeng Zhang |
| author_facet | Lilian Huang Wenju Yao Jianhong Xiang Zefeng Zhang |
| author_sort | Lilian Huang |
| collection | DOAJ |
| description | In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation. |
| format | Article |
| id | doaj-art-eba9fb4b2dff4446b763e3f9200d2056 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-eba9fb4b2dff4446b763e3f9200d20562025-02-03T01:04:15ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/24084602408460Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation DiagramsLilian Huang0Wenju Yao1Jianhong Xiang2Zefeng Zhang3College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, ChinaIn this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.http://dx.doi.org/10.1155/2020/2408460 |
| spellingShingle | Lilian Huang Wenju Yao Jianhong Xiang Zefeng Zhang Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams Complexity |
| title | Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams |
| title_full | Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams |
| title_fullStr | Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams |
| title_full_unstemmed | Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams |
| title_short | Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams |
| title_sort | heterogeneous and homogenous multistabilities in a novel 4d memristor based chaotic system with discrete bifurcation diagrams |
| url | http://dx.doi.org/10.1155/2020/2408460 |
| work_keys_str_mv | AT lilianhuang heterogeneousandhomogenousmultistabilitiesinanovel4dmemristorbasedchaoticsystemwithdiscretebifurcationdiagrams AT wenjuyao heterogeneousandhomogenousmultistabilitiesinanovel4dmemristorbasedchaoticsystemwithdiscretebifurcationdiagrams AT jianhongxiang heterogeneousandhomogenousmultistabilitiesinanovel4dmemristorbasedchaoticsystemwithdiscretebifurcationdiagrams AT zefengzhang heterogeneousandhomogenousmultistabilitiesinanovel4dmemristorbasedchaoticsystemwithdiscretebifurcationdiagrams |