Chaotic Dynamics by Some Quadratic Jerk Systems
This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter <i>a</i>. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attrac...
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MDPI AG
2021-09-01
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/227 |
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| author | Mei Liu Bo Sang Ning Wang Irfan Ahmad |
| author_facet | Mei Liu Bo Sang Ning Wang Irfan Ahmad |
| author_sort | Mei Liu |
| collection | DOAJ |
| description | This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter <i>a</i>. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems. |
| first_indexed | 2024-03-10T07:53:11Z |
| format | Article |
| id | doaj.art-552f8fc260b74850b0553611c58eb107 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:53:11Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-552f8fc260b74850b0553611c58eb1072023-11-22T12:03:17ZengMDPI AGAxioms2075-16802021-09-0110322710.3390/axioms10030227Chaotic Dynamics by Some Quadratic Jerk SystemsMei Liu0Bo Sang1Ning Wang2Irfan Ahmad3School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaSchool of Electrical and Information Engineering, Tianjin University, Tianjin 300072, ChinaSirindhorn International Institute of Technology, Thammasat University, Pathum Thani 12000, ThailandThis paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter <i>a</i>. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems.https://www.mdpi.com/2075-1680/10/3/227Hopf bifurcationlimit cycleperiod-doubling cascadeself-excited attractorhidden attractor |
| spellingShingle | Mei Liu Bo Sang Ning Wang Irfan Ahmad Chaotic Dynamics by Some Quadratic Jerk Systems Axioms Hopf bifurcation limit cycle period-doubling cascade self-excited attractor hidden attractor |
| title | Chaotic Dynamics by Some Quadratic Jerk Systems |
| title_full | Chaotic Dynamics by Some Quadratic Jerk Systems |
| title_fullStr | Chaotic Dynamics by Some Quadratic Jerk Systems |
| title_full_unstemmed | Chaotic Dynamics by Some Quadratic Jerk Systems |
| title_short | Chaotic Dynamics by Some Quadratic Jerk Systems |
| title_sort | chaotic dynamics by some quadratic jerk systems |
| topic | Hopf bifurcation limit cycle period-doubling cascade self-excited attractor hidden attractor |
| url | https://www.mdpi.com/2075-1680/10/3/227 |
| work_keys_str_mv | AT meiliu chaoticdynamicsbysomequadraticjerksystems AT bosang chaoticdynamicsbysomequadraticjerksystems AT ningwang chaoticdynamicsbysomequadraticjerksystems AT irfanahmad chaoticdynamicsbysomequadraticjerksystems |