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Ensembles of excitable two-state units with delayed feedback
Nikos Kouvaris1, Felix Müller, Lutz Schimansky-Geier
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
This study models excitable systems using a two-state unit with non-Markovian dynamics. It reveals complex bifurcations and oscillations in globally coupled ensembles, influenced by noise and time-delayed feedback.
Area of Science:
- Theoretical physics
- Nonlinear dynamics
- Complex systems
Background:
- Excitable systems are fundamental in various scientific fields.
- Modeling these systems often employs Markovian approaches.
- Non-Markovian dynamics offer a more nuanced description of system states.
Purpose of the Study:
- To develop a non-Markovian model for excitable systems using a two-state unit.
- To analyze the dynamics of globally coupled ensembles of these units.
- To investigate bifurcations and emergent phenomena like oscillations.
Main Methods:
- Abstract modification of excitable systems into two-state units.
- Non-Markovian approach with distinct waiting time distributions.
- Derivation of mean-field equations for coupled ensembles.
- Analysis of bifurcations (saddle-node, pitchfork, Hopf) and oscillations.
Main Results:
- Exact formulas for interspike interval distribution and power spectral density.
- Identification of saddle-node and pitchfork bifurcations dependent on coupling and noise.
- Emergence of bulk oscillations via Hopf bifurcations with time-delayed feedback.
Conclusions:
- The non-Markovian two-state model accurately captures complex dynamics in excitable systems.
- Coupling strength, noise intensity, and feedback delay critically influence system behavior and bifurcations.
- Coherent activation events and bulk oscillations arise under specific conditions of delayed feedback.
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