TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

WoS  JIF 2026 : 0.5 (Q3)

Powered by:Powered by

Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

Issues up to 2022 co-published with and available at:Taylor & Francis
info@tarupublications.com
Open Access Research Article

Design of multistable behaviour using speed feedback controller for coupled chaotic systems with mismatch parameters

* , ,

* Corresponding author · click or hover a name for details

pp. 45–57Vol. 23Issue 1 & 2November 2025DOI: 10.47974/JDSGT-2024-011XML
Received:
13 Nov 2024
Published Online:
29 Nov 2025
Article type:
Research Article
Language:
EN
Article no.:
JDSGT-2024-011
Pages:
45–57

Abstract

Multistable behavior typically refers to a system that has multiple stable states. To achieve multistability using speed feedback controller, we consider two different Lorenz and Rossler chaotic systems respectively and also find extreme multistability by considering identical coupled chaotic Chen system with mismatch parameters. Numerical simulation outcomes are explained to exhibit the functional capability of the recommended framework to create highly stable multi-state synchronization performance. This work displays a theoretical base for building utmost multistable system for continuous system. 

Keywords

Subject Classifications

26A1828Dxx34Cxx34Dxx35Bxx46Lxx58Jxx70-XX

References

[1] F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, “Experimental evidence of subharmonic bifurcations, multistability and turbulence in Q-switched gas laser,” Phys. Rev. Lett., vol. 49, pp. 1217-1220 (1982).
[2] S. A. Beznosyuk, B. F. Minaev, and Z. M. Muldakhmetov, “Informative energetic structure and electronic multistability of condensed state,” J. Mol. Struct. THEOCHEM, vol. 227, pp. 125-129 (1991).
[3] M. S. Patel, U. Patel, A. Sen, G. C. Sethia, C. Hens, S. K. Dana, and R. E. Amritkar, “Experimental observation of extreme multistability in an electronic system of two coupled Rossler oscillators,” Phys. Rev. E, vol. 89, no. 2, p. 022918 (2014).
[4] E. Ullner, A. Zaikin, E. I. Volkov, and J. Garcia-Ojalvo, “Multistability and clustering in a population of synthetic genetic oscillators via phase-repulsive cell-to-cell communication,” Phys. Rev. Lett., vol. 99, no. 14, p. 148103 (2007).
[5] M. I. Rabinovich, P. Varona, A. I. Selverston, and H. D. Abarbanel, “Dynamical principles in neuroscience,” Rev. Mod. Phys., vol. 78, no. 4, p. 1213 (2006).
[6] R. Calov and A. Ganopolski, “Multistability and hysteresis in the climate cryosphere system under orbital forcing,” Geophys. Res. Lett., vol. 32, no. 21 (2005).
[7] H. Sun, S. K. Scott, and K. Showalter, “Uncertain destination dynamics,” Phys. Rev. E, vol. 60, pp. 3876-3880 (1999).
[8] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett., vol. 64, pp. 821-824 (1990).
[9] U. Feudel and C. Grebogi, “Multistability and the control of complexity,” Chaos, vol. 7, no. 4, pp. 597-604 (1997).
[10] A. T. Layton, L. C. Moore, and H. E. Layton, “Multistability in tubuloglomerular feedback and spectral complexity in spontaneously hypertensive rats,” Am. J. Physiol. Renal Physiol., vol. 291, no. 1, pp. F79-F97 (2006).
[11] A. Geltrude, K. Al Naimee, S. Euzzor, R. Meucci, F. T. Arecchi, and B. K. Goswami, “Feedback control of bursting and multistability in chaotic systems,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 7, pp. 3031-3039 (2012).
[12] C. Li, W. Hu, J. C. Sprott, and X. Wang, “Multistability in symmetric chaotic systems,” Eur. Phys. J. Spec. Top., vol. 224, no. 8, pp. 1493-1506 (2015).
[13] C. Hens, S. K. Dana, and U. Feudel, “Extreme multistability: Attractor manipulation and robustness,” Chaos, vol. 25, no. 5, p. 053112 (2015). 
[14] S. Pal, B. Sahoo, and S. Poria, “Multistable behaviour of coupled Lorenz–Stenflo systems,” Physica Scripta, vol. 89, 045202 (2014).
[15] B. C. Bao, H. Bao, N. Wang, M. Chen, and Q. Xu, “Hidden extreme multistability in memristive hyperchaotic system,” Chaos Solitons Fractals, vol. 94, pp. 102-111 (2017).
[16] M. A. Khan, M. Nag, and S. Poria, “Design of multistable systems via partial synchronization,” Pramana, vol. 89, no. 2, p. 19 (2017).
[17] M. F. Abdul Rahim, H. Natiq, N. A. A. Fataf, and S. Banerjee, “Dynamics of a new hyperchaotic system and multistability,” Eur. Phys. J. Plus, vol. 134, pp. 1-9 (2019).
[18] H. Chang, Y. Li, G. Chen, and F. Yuan, “Extreme multistability and complex dynamics of a memristor-based chaotic system,” Int. J. Bifurcation Chaos, vol. 30, no. 08, p. 2030019 (2020).
[19] A. N. Pisarchik and U. Feudel, “Control of multistability,” Phys. Rep., vol. 540, no. 4, pp. 167-218 (2014).
[20] F. Yuan, G. Wang, and X. Wang, “Extreme multistability in a memristor-based multi-scroll hyper-chaotic system,” Chaos, vol. 26, no. 7 (2016).
[21] S. Zhang, Y. Zeng, Z. Li, M. Wang, and L. Xiong, “Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability,” Chaos, vol. 28, no. 1 (2018).
[22] X. Wang, N. V. Kuznetsov, and G. Chen, Eds., Chaotic Systems with Multistability and Hidden Attractors, vol. 40. Cham, Switzerland: Springer, pp. 149-150 (2021).

Views: 157Downloads: 68Citations: 0