Critical dynamics of the Bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation
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Publication:688178
DOI10.1016/0167-2789(93)90084-EzbMath0779.34032MaRDI QIDQ688178
Barteld Braaksma, Johan Grasman
Publication date: 30 November 1993
Published in: Physica D (Search for Journal in Brave)
chaotic behaviorbifurcation diagramsexcitable systemsperiodic stimulusbiological and physiological applicationsBonhoeffer-van der Pol equation
Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Dynamical systems and ergodic theory (37-XX)
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Cites Work
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- A deterministic model of the cell cycle
- Asymptotic methods for relaxation oscillations and applications
- Stochastic and chaotic relaxation oscillations
- Effect of noise and perturbations on limit cycle systems
- Phantom ducks and models of excitability
- On the Resonance Structure in a Forced Excitable System
- Singular Hopf Bifurcation to Relaxation Oscillations
- Relaxation oscillations including a standard chase on French ducks
