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Thresholds of excitability in three-dimensional dynamical systems.
Michal Voslar1, Igor Schreiber
1Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical Technology, Technická 5, 166 28 Prague 6, Czech Republic.
Summary
Researchers developed a novel method to map threshold surfaces in excitable systems by calculating threshold trajectories. This technique effectively models complex biochemical oscillators and can be generalized to higher dimensions.
Area of Science:
- * Computational modeling
- * Nonlinear dynamics
- * Biochemical systems
Background:
- * Excitable systems are crucial in various scientific fields, including biology and physics.
- * Understanding their dynamics often requires identifying critical thresholds.
- * Existing methods may not fully capture the complexity of these thresholds.
Purpose of the Study:
- * To introduce a new computational method for determining the threshold surface in two-dimensional excitable systems.
- * To apply this method to a biochemical oscillator model with positive feedback loops.
- * To explore the generalizability of the technique to higher-dimensional systems.
Main Methods:
- * Calculation of threshold trajectories in phase space cross-sections.
- * Formulation and numerical solution of a nonlinear boundary value problem.
- * Utilization of adaptive multiple shooting and continuation methods for solving the problem.
- * Application to a biochemical oscillator model with two positive feedbacks.
Main Results:
- * Successfully determined a two-dimensional threshold surface for the excitable system.
- * Demonstrated the efficacy of the numerical approach for solving the complex boundary value problem.
- * Provided a validated model for a biochemical oscillator with two positive feedbacks.
Conclusions:
- * The developed method provides a robust way to define and calculate threshold surfaces in excitable systems.
- * The technique is applicable to complex systems like biochemical oscillators.
- * The approach is generalizable to systems of arbitrary dimensions, offering broad applicability.