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Construction of quasipotentials for stochastic dynamical systems: An optimization approach
R D Brackston1, A Wynn2, M P H Stumpf1,3
1Department of Life Sciences, Imperial College London, London SW7 2AZ, United Kingdom.
Physical Review. E
|September 27, 2018
Summary
Researchers developed a new method to construct potential landscapes for stochastic dynamical systems. This approach uses control theory to analytically derive the quasipotential, offering bounds on system dynamics.
Area of Science:
- Dynamical Systems Theory
- Control Theory
- Computational Mathematics
Background:
- Constructing landscapes for stochastic dynamical systems is complex.
- The quasipotential quantifies state-space exploration likelihood.
- Langevin equations often describe system dynamics.
Purpose of the Study:
- To present a novel analytical method for constructing potential landscapes.
- To provide bounds on the quasipotential for stochastic systems.
- To apply control theory tools to dynamical systems analysis.
Main Methods:
- Extended the sum-of-squares method from control theory.
- Utilized convex optimization to find polynomial landscape coefficients.
- Decomposed system dynamics into potential gradient and curl components.
Main Results:
- Developed an analytical polynomial expression for potential landscapes.
- Derived landscapes provide upper and lower bounds on the quasipotential.
- Method validated on high-dimensional linear and nonlinear systems.
Conclusions:
- The sum-of-squares method offers an effective approach to landscape construction.
- The derived landscapes provide valuable insights into system behavior.
- This method is applicable to polynomial-described dynamical systems.
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