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Chaotic Dynamics and Control of a Discrete‐Time Chen System

Author

Listed:
  • Sarker Md. Sohel Rana
  • Md. Jasim Uddin
  • P. K. Santra
  • G. S. Mahapatra

Abstract

We investigate a discrete‐time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD‐NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0‐1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system.

Suggested Citation

  • Sarker Md. Sohel Rana & Md. Jasim Uddin & P. K. Santra & G. S. Mahapatra, 2023. "Chaotic Dynamics and Control of a Discrete‐Time Chen System," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:7795246
    DOI: 10.1155/2023/7795246
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    References listed on IDEAS

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    1. Baogui Xin & Zhiheng Wu, 2015. "Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area," Sustainability, MDPI, vol. 7(8), pages 1-19, July.
    2. Abdelaziz, Mahmoud A.M. & Ismail, Ahmad Izani & Abdullah, Farah A. & Mohd, Mohd Hafiz, 2020. "Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Alasty, Aria & Salarieh, Hassan, 2007. "Nonlinear feedback control of chaotic pendulum in presence of saturation effect," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 292-304.
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