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A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing

Author

Listed:
  • Arthanari Ramesh
  • Alireza Bahramian
  • Hayder Natiq
  • Karthikeyan Rajagopal
  • Sajad Jafari
  • Iqtadar Hussain

Abstract

This work introduces a three‐dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self‐excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system.

Suggested Citation

  • Arthanari Ramesh & Alireza Bahramian & Hayder Natiq & Karthikeyan Rajagopal & Sajad Jafari & Iqtadar Hussain, 2022. "A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:6279373
    DOI: 10.1155/2022/6279373
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    References listed on IDEAS

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    1. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    2. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    3. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    4. Frank Hellmann & Paul Schultz & Patrycja Jaros & Roman Levchenko & Tomasz Kapitaniak & Jürgen Kurths & Yuri Maistrenko, 2020. "Network-induced multistability through lossy coupling and exotic solitary states," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    5. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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