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Periodicity suppression in continuous-time dynamical systems by external forcing
Amanda C Mathias1, Paulo C Rech
1Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil. amaandafisica@gmail.com
Chaos (Woodbury, N.Y.)
|January 3, 2013
Summary
External periodic forcing can suppress periodicity in chaotic systems. Numerical simulations demonstrate that even embedded periodic windows can be entirely eliminated by adjusting forcing amplitude.
Area of Science:
- Nonlinear dynamics
- Fluid mechanics
- Chaos theory
Background:
- Autonomous nonlinear systems often exhibit complex dynamics, including chaos.
- External periodic forcing is a common method to influence system behavior.
- Understanding the interplay between intrinsic dynamics and external perturbations is crucial.
Purpose of the Study:
- To investigate the suppression of periodicity in nonlinear systems subjected to external periodic forcing.
- To determine the conditions under which periodic behaviors embedded within chaotic attractors can be eliminated.
- To analyze the impact of forcing amplitude on periodicity suppression.
Main Methods:
- Modeling fluid flows using sets of three autonomous nonlinear first-order ordinary differential equations.
- Performing numerical simulations to explore system dynamics.
- Utilizing parameter plane plots, phase-space portraits, and largest Lyapunov exponent calculations to characterize system behavior.
Main Results:
- Demonstrated that external periodic forcing can lead to the complete suppression of periodicity.
- Identified that windows of periodicity embedded within chaotic regions are susceptible to suppression.
- Showed that varying the amplitude of sinusoidal forcing significantly affects the presence of periodic behavior.
Conclusions:
- External periodic forcing is an effective tool for suppressing inherent periodicity in nonlinear systems.
- The amplitude of the applied forcing is a critical parameter in determining the extent of periodicity suppression.
- These findings have implications for controlling chaotic behavior in various physical systems.
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