Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, , 98 - 103, 30.06.2023

Paulo Rech

https://doi.org/10.33434/cams.1218552

Öz

Kaynakça

  • [1] J. C. Sprott, Elegant chaos: Algebraically simple chaotic flows, World Scientific, Singapore, 2010.
  • [2] K. Rajagopal, A. Akgul, V. T. Pham, F. E. Alsaadi, F. Nazarimehr, E. Alsaadi, S. Jafari, Multistability and coexisting attractors in a new circulant chaotic system, Int. J. Bifurc. Chaos 29 (2019), 1950174.
  • [3] A. Wolf , J. B. Swift, H. L. Swinney, J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D, 16 (1985), 285–317.
  • [4] U. Feudel, C. Grebogi, Multistability and the control of complexity, Chaos 7 (1997), 597–604.
  • [5] S. M. Hammel, C. K. R. T. Jones, J. V. Moloney, Global dynamical behavior of the optical field in a ring cavity, J. Opt. Soc. Am. B 2 (1985), 552–564.
  • [6] P. Marmillot, M. Kaufman, J. Hervagault, Multiple steady states and dissipative structures in a circular and linear array of three cells: Numerical and experimental approaches, J. Chem. Phys. 95 (1991), 1206–1214.
  • [7] S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, W. L. Ditto, Controlling chaos in the brain, Nature 370 (1994), 615–620.
  • [8] F. Prengel, A. Wacker, E. Sch¨oll, Simple model for multistability and domain formation in semiconductor superlattices, Phys. Rev. B 50 (1994), 1705–1712.
  • [9] S. Yoden, Classification of simple low-order models in geophysical fluid dynamics and climate dynamics, Nonlinear Anal. Methods Appl. 30 (1997), 4607–4618.
  • [10] S. Zhang, J. Zheng, X. Wang, Z. Zeng, A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability, Chaos Solitons Fractals 145 (2021), 110761.
  • [11] C. Gao, S. Qiao, X. An, Global multistability mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model, Chaos Solitons Fractals 160 (2022), 112281.
  • [12] L. Zhu, M. Pan, Hyperchaotic oscillation and multistability in a fourth order smooth Chua system with Implementation using no analog multipliers, Int. J. Bifurc. Chaos 32 (2022), 2250185.
  • [13] I. Ahmad, B. Srisuchinwong, M. U. Jamil, Coexistence of Hidden attractors in the smooth cubic Chua’s circuit with two stable equilibria, Int. J. Bifurc. Chaos 33 (2023), 2330010.
  • [14] H. Bao, Y. Gu, Q. Xu, X. Zhang, B. Bao, Parallel bi-memristor hyperchaotic map with extreme multistability, Chaos Solitons Fractals 160 (2022), 112273.
  • [15] B. Spagnolo, A. A. Dubkov, A. Carollo, D. Valenti, Memristors and nonequilibrium stochastic multistable systems, Chaos Solitons Fractals 164 (2022), 112610.
  • [16] B. G. Rajni, Multistability, chaos and mean population density in a discrete-time predator–prey system, Chaos Solitons Fractals 162 (2022), 112497.
  • [17] P. P. Singh, B. K. Roy, Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria, Chaos Solitons Fractals 161 (2022), 112312.
  • [18] S. T. Tanekou, J. Ramadoss, J. Kengne, G. D. Kenmoe, K. Rajagopal, Coexistence of periodic, chaotic and hyperchaotic attractors in a system consisting of a Duffing Oscillator coupled to a Van der Pol Oscillator, Int. J. Bifurc. Chaos 33 (2023), 2330004.
  • [19] V. Wiggers, P. C. Rech, On the dynamics of a Van der Pol-Duffing snap system, Eur. Phys. J. B 95 (2022), 28.
  • [20] P. C. Rech, Self-excited and hidden attractors in a multistable jerk system, Chaos Solitons Fractals 164 (2022), 112614.

Multistability in a Circulant Dynamical System

Yıl 2023, , 98 - 103, 30.06.2023

Paulo Rech

https://doi.org/10.33434/cams.1218552

Öz

In this paper we report on a two parameter four-dimensional dynamical system with cyclic symmetry, namely a circulant dynamical system. This system is a twelve-term polynomial system with four cubic nonlinearities. Reported are some parameter-space diagrams for this system, all of them considering the same range of parameters, but generated from different initial conditions. We show that such diagrams display the occurrence of multistability in this system. Properly generated bifurcation diagrams confirm this finding. Basins of attraction of coexisting attractors in the related phase-space are presented, as well as an example showing phase portraits for periodic and chaotic coexisting attractors.

Anahtar Kelimeler

Basin of attraction Circulant dynamical system Multistability Parameter-space

Kaynakça

  • [1] J. C. Sprott, Elegant chaos: Algebraically simple chaotic flows, World Scientific, Singapore, 2010.
  • [2] K. Rajagopal, A. Akgul, V. T. Pham, F. E. Alsaadi, F. Nazarimehr, E. Alsaadi, S. Jafari, Multistability and coexisting attractors in a new circulant chaotic system, Int. J. Bifurc. Chaos 29 (2019), 1950174.
  • [3] A. Wolf , J. B. Swift, H. L. Swinney, J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D, 16 (1985), 285–317.
  • [4] U. Feudel, C. Grebogi, Multistability and the control of complexity, Chaos 7 (1997), 597–604.
  • [5] S. M. Hammel, C. K. R. T. Jones, J. V. Moloney, Global dynamical behavior of the optical field in a ring cavity, J. Opt. Soc. Am. B 2 (1985), 552–564.
  • [6] P. Marmillot, M. Kaufman, J. Hervagault, Multiple steady states and dissipative structures in a circular and linear array of three cells: Numerical and experimental approaches, J. Chem. Phys. 95 (1991), 1206–1214.
  • [7] S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, W. L. Ditto, Controlling chaos in the brain, Nature 370 (1994), 615–620.
  • [8] F. Prengel, A. Wacker, E. Sch¨oll, Simple model for multistability and domain formation in semiconductor superlattices, Phys. Rev. B 50 (1994), 1705–1712.
  • [9] S. Yoden, Classification of simple low-order models in geophysical fluid dynamics and climate dynamics, Nonlinear Anal. Methods Appl. 30 (1997), 4607–4618.
  • [10] S. Zhang, J. Zheng, X. Wang, Z. Zeng, A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability, Chaos Solitons Fractals 145 (2021), 110761.
  • [11] C. Gao, S. Qiao, X. An, Global multistability mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model, Chaos Solitons Fractals 160 (2022), 112281.
  • [12] L. Zhu, M. Pan, Hyperchaotic oscillation and multistability in a fourth order smooth Chua system with Implementation using no analog multipliers, Int. J. Bifurc. Chaos 32 (2022), 2250185.
  • [13] I. Ahmad, B. Srisuchinwong, M. U. Jamil, Coexistence of Hidden attractors in the smooth cubic Chua’s circuit with two stable equilibria, Int. J. Bifurc. Chaos 33 (2023), 2330010.
  • [14] H. Bao, Y. Gu, Q. Xu, X. Zhang, B. Bao, Parallel bi-memristor hyperchaotic map with extreme multistability, Chaos Solitons Fractals 160 (2022), 112273.
  • [15] B. Spagnolo, A. A. Dubkov, A. Carollo, D. Valenti, Memristors and nonequilibrium stochastic multistable systems, Chaos Solitons Fractals 164 (2022), 112610.
  • [16] B. G. Rajni, Multistability, chaos and mean population density in a discrete-time predator–prey system, Chaos Solitons Fractals 162 (2022), 112497.
  • [17] P. P. Singh, B. K. Roy, Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria, Chaos Solitons Fractals 161 (2022), 112312.
  • [18] S. T. Tanekou, J. Ramadoss, J. Kengne, G. D. Kenmoe, K. Rajagopal, Coexistence of periodic, chaotic and hyperchaotic attractors in a system consisting of a Duffing Oscillator coupled to a Van der Pol Oscillator, Int. J. Bifurc. Chaos 33 (2023), 2330004.
  • [19] V. Wiggers, P. C. Rech, On the dynamics of a Van der Pol-Duffing snap system, Eur. Phys. J. B 95 (2022), 28.
  • [20] P. C. Rech, Self-excited and hidden attractors in a multistable jerk system, Chaos Solitons Fractals 164 (2022), 112614.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik, Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler
Bölüm Makaleler
Yazarlar

Paulo Rech 0000-0003-2235-0469

Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 13 Aralık 2022
Kabul Tarihi 22 Mayıs 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Rech, P. (2023). Multistability in a Circulant Dynamical System. Communications in Advanced Mathematical Sciences, 6(2), 98-103. https://doi.org/10.33434/cams.1218552
AMA Rech P. Multistability in a Circulant Dynamical System. Communications in Advanced Mathematical Sciences. Haziran 2023;6(2):98-103. doi:10.33434/cams.1218552
Chicago Rech, Paulo. “Multistability in a Circulant Dynamical System”. Communications in Advanced Mathematical Sciences 6, sy. 2 (Haziran 2023): 98-103. https://doi.org/10.33434/cams.1218552.
EndNote Rech P (01 Haziran 2023) Multistability in a Circulant Dynamical System. Communications in Advanced Mathematical Sciences 6 2 98–103.
IEEE P. Rech, “Multistability in a Circulant Dynamical System”, Communications in Advanced Mathematical Sciences, c. 6, sy. 2, ss. 98–103, 2023, doi: 10.33434/cams.1218552.
ISNAD Rech, Paulo. “Multistability in a Circulant Dynamical System”. Communications in Advanced Mathematical Sciences 6/2 (Haziran 2023), 98-103. https://doi.org/10.33434/cams.1218552.
JAMA Rech P. Multistability in a Circulant Dynamical System. Communications in Advanced Mathematical Sciences. 2023;6:98–103.
MLA Rech, Paulo. “Multistability in a Circulant Dynamical System”. Communications in Advanced Mathematical Sciences, c. 6, sy. 2, 2023, ss. 98-103, doi:10.33434/cams.1218552.
Vancouver Rech P. Multistability in a Circulant Dynamical System. Communications in Advanced Mathematical Sciences. 2023;6(2):98-103.

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