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A bifurcation giving birth to order in an impulsively driven complex system
1Indian Institute of Technology Madras, Chennai, India.
Chaos (Woodbury, N.Y.)
|September 3, 2016
Summary
This study explores nonlinear oscillators with impulsive forcing, revealing how discontinuity-induced bifurcations drive transitions from chaotic to periodic oscillations in turbulent combustion systems.
Area of Science:
- Complex Systems Dynamics
- Nonlinear Oscillations
- Turbulent Combustion
Background:
- Nonlinear oscillations are fundamental to many complex systems.
- Impulsive forcing is a common phenomenon in various natural and engineered systems.
- Understanding the behavior of nonlinear oscillators under such forcing is crucial.
Purpose of the Study:
- To investigate the dynamics of nonlinear oscillators subjected to impulsive forcing.
- To model these systems as piecewise smooth dynamical systems.
- To apply this framework to understand pattern formation in turbulent combustion.
Main Methods:
- Modeling kicked oscillatory systems as piecewise smooth dynamical systems.
- Analyzing discontinuity-induced bifurcations.
- Investigating transitions between chaotic and periodic oscillation regimes.
Main Results:
- Identified discontinuity-induced bifurcations as the mechanism for transitions from low-amplitude chaotic to large-amplitude periodic oscillations.
- Explained the occurrence of intermittent oscillations in turbulent combustion systems.
- Provided a formalism for analyzing pattern formation in these systems.
Conclusions:
- Piecewise smooth dynamical systems provide a valuable framework for studying impulsively forced nonlinear oscillators.
- Discontinuity-induced bifurcations play a significant role in the complex dynamics observed in systems like turbulent combustion.
- The study offers insights into pattern formation and oscillation intermittency in turbulent combustion.
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