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Stabilization in chaotic maps using hybrid chaos control procedure.

Ashish1, Mohammad Sajid2

  • 1Department of Mathematics, Government College Satnali, Mahendergarh, 123024, India.

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Summary
This summary is machine-generated.

This study introduces a novel hybrid method to control chaos in discrete population growth models. The procedure stabilizes chaotic systems at desired periodic states, offering flexibility and novel control strategies.

Keywords:
Bifurcation plotChaos controlLyapunov exponentNonlinear systemsNumerical results

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Mathematical Biology

Background:

  • Chaos control in nonlinear systems is a significant research area.
  • Existing methods for chaos control have limitations in discrete systems.

Purpose of the Study:

  • To develop a novel hybrid chaos control procedure for discrete chaotic systems.
  • To stabilize chaos in population growth models at globally accepted stable equilibria.

Main Methods:

  • A new hybrid control procedure is derived.
  • The method is applied to discrete chaotic equations of population growth models.
  • Numerical simulations including bifurcation plots and time-series analyses are used.

Main Results:

  • The hybrid procedure effectively stabilizes chaos in discrete population growth models.
  • The method allows stabilization at various periodic states (order p) by adjusting parameters.
  • The approach offers simplicity and flexibility in achieving desired stability.

Conclusions:

  • The novel hybrid chaos control method is effective and versatile.
  • This approach provides a new tool for controlling chaos in discrete dynamical systems.
  • The findings have implications for understanding and managing complex population dynamics.