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Chaos and intermittent bursting in a reaction-diffusion process.
Ira B. Schwartz1, Ioana Triandaf
1Special Project in Nonlinear Science, U.S. Naval Research Laboratory Code 6700.3, Plasma Physics Division, Washington, D.C. 20375-5000Science Applications International, Corporation, Applied Physics Operation, McLean, Virginia 22102.
Chaos (Woodbury, N.Y.)
|June 1, 1996
Summary
Karhunen-Loeve decomposition simplifies chaotic chemical reactions. This method creates a low-dimensional model capturing key behaviors like intermittent bursts and chaos transitions.
Area of Science:
- Chemical Engineering
- Nonlinear Dynamics
- Computational Chemistry
Background:
- Chemical processes in open reactors can exhibit complex spatio-temporal dynamics.
- Nonlinear reaction-diffusion models are crucial for understanding these systems.
- Characterizing chaotic behavior and transitions is essential for process control.
Purpose of the Study:
- To apply Karhunen-Loeve decomposition to a chaotic reaction-diffusion system.
- To derive a low-dimensional ordinary differential equation (ODE) model from a partial differential equation (PDE) model.
- To analyze the chaotic dynamics and bifurcations in the reduced model.
Main Methods:
- Karhunen-Loeve decomposition of spatio-temporal solutions.
- Galerkin projection of dominant modes onto the PDE system.
- Analysis of the resulting ODE model for chaotic behavior and bifurcations.
Main Results:
- A low-dimensional ODE model accurately represents the chaotic dynamics of the original PDE model.
- The reduced model captures intermittent bursting and transitions to chaos.
- Saddle-node bifurcations are identified as the mechanism for intermittent bursts and oscillations.
Conclusions:
- Karhunen-Loeve decomposition is effective for model reduction of complex chemical systems.
- The low-dimensional model provides insights into the onset and nature of chaos.
- Understanding bifurcations aids in predicting and controlling chaotic chemical processes.