Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function
In this paper, we construct an inertial two-neuron system with a non-monotonic activation function. Theoretical analysis and numerical simulation are employed to illustrate the complex dynamics. It is found that the neural system exhibits the mixed coexistence with periodic orbits and chaotic attrac...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/10.3934/mbe.2019320?viewType=HTML |
| _version_ | 1828366040123310080 |
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| author | Zigen Song Jian Xu Bin Zhen |
| author_facet | Zigen Song Jian Xu Bin Zhen |
| author_sort | Zigen Song |
| collection | DOAJ |
| description | In this paper, we construct an inertial two-neuron system with a non-monotonic activation function. Theoretical analysis and numerical simulation are employed to illustrate the complex dynamics. It is found that the neural system exhibits the mixed coexistence with periodic orbits and chaotic attractors. To this end, the equilibria and their stability are analyzed. The system parameters are divided into some regions with the different number of equilibria by the static bifurcation curve. Then, employing some numerical simulations, including the phase portraits, Lyapunov exponents, bifurcation diagrams, and the sensitive dependence to initial values, we find that the system generates two coexisting single-scroll chaotic attractors via the period-doubling bifurcation. Further, the single-scroll chaos will evolve into the double-scroll chaotic attractor. Finally, to view the global evolutions of dynamical behavior, we employ the combined bifurcation diagrams including equilibrium points and periodic orbits. Many types of multistability are presented, such as the bistable periodic orbits, multistable periodic orbits, and multistable chaotic attractors with multi-periodic orbits. The phase portraits and attractor basins are shown to verify the coexisting attractors. Additionally, transient chaos in neural system is observed by phase portraits and time histories. |
| first_indexed | 2024-04-14T05:39:52Z |
| format | Article |
| id | doaj.art-fdaffc1e439c41949297ecf5fc60776b |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-14T05:39:52Z |
| publishDate | 2019-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-fdaffc1e439c41949297ecf5fc60776b2022-12-22T02:09:30ZengAIMS PressMathematical Biosciences and Engineering1551-00182019-07-011666406642510.3934/mbe.2019320Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation functionZigen Song0Jian Xu1Bin Zhen21. College of Information Technology, Shanghai Ocean University, Shanghai, 201306, P.R. China2. School of Aerospace and Mechanics Engineering, Tongji University, Shanghai 200092, P.R. China3. School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, P.R. ChinaIn this paper, we construct an inertial two-neuron system with a non-monotonic activation function. Theoretical analysis and numerical simulation are employed to illustrate the complex dynamics. It is found that the neural system exhibits the mixed coexistence with periodic orbits and chaotic attractors. To this end, the equilibria and their stability are analyzed. The system parameters are divided into some regions with the different number of equilibria by the static bifurcation curve. Then, employing some numerical simulations, including the phase portraits, Lyapunov exponents, bifurcation diagrams, and the sensitive dependence to initial values, we find that the system generates two coexisting single-scroll chaotic attractors via the period-doubling bifurcation. Further, the single-scroll chaos will evolve into the double-scroll chaotic attractor. Finally, to view the global evolutions of dynamical behavior, we employ the combined bifurcation diagrams including equilibrium points and periodic orbits. Many types of multistability are presented, such as the bistable periodic orbits, multistable periodic orbits, and multistable chaotic attractors with multi-periodic orbits. The phase portraits and attractor basins are shown to verify the coexisting attractors. Additionally, transient chaos in neural system is observed by phase portraits and time histories.https://www.aimspress.com/article/10.3934/mbe.2019320?viewType=HTMLinertial neuron systemnonmonotonic activation functionmultistabilityattractor merging crisisperiod-doubling bifurcationtransient chaos |
| spellingShingle | Zigen Song Jian Xu Bin Zhen Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function Mathematical Biosciences and Engineering inertial neuron system nonmonotonic activation function multistability attractor merging crisis period-doubling bifurcation transient chaos |
| title | Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| title_full | Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| title_fullStr | Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| title_full_unstemmed | Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| title_short | Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| title_sort | mixed coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function |
| topic | inertial neuron system nonmonotonic activation function multistability attractor merging crisis period-doubling bifurcation transient chaos |
| url | https://www.aimspress.com/article/10.3934/mbe.2019320?viewType=HTML |
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