Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer-van der Pol oscillator
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Publication:2083700
DOI10.1016/j.physd.2022.133438OpenAlexW4285014769MaRDI QIDQ2083700
Kaito Kato, Kuniyasu Shimizu, Takuji Kousaka, Hideaki Okazaki, Naohiko Inaba
Publication date: 11 October 2022
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2022.133438
supercritical Hopf bifurcationweak periodic perturbationmixed-mode oscillation-incrementing bifurcation
Bifurcations and instability for nonlinear problems in mechanics (70K50) General perturbation schemes for nonlinear problems in mechanics (70K60)
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Nested mixed-mode oscillations in the forced van der Pol oscillator ⋮ Nested mixed-mode oscillations. III: Comparison of bifurcation structures between a driven Bonhoeffer-van der Pol oscillator and Nagumo-Sato piecewise-linear discontinuous one-dimensional map
Cites Work
- Unnamed Item
- Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator
- Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems
- Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation
- Multiple time scale dynamics
- Three time-scales in an extended Bonhoeffer-van der Pol oscillator
- Critical dynamics of the Bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation
- Multimodal oscillations in systems with strong contraction
- Local analysis near a folded saddle-node singularity
- A Bonhoeffer-van der Pol oscillator model of locked and non-locked behaviors of living pacemaker neurons
- Global bifurcation structure of a Bonhoeffer-van der Pol oscillator driven by periodic pulse trains. Comparison with data from a periodically inhibited biological pacemaker
- Response characteristics of the BVP neuron model to periodic pulse inputs
- The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains
- Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation
- Nested mixed-mode oscillations. II: Experimental and numerical study of a classical Bonhoeffer-van der Pol oscillator
- Nested mixed-mode oscillations
- Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation
- NUMERICAL COMPUTATION OF CANARDS
- Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
- Mixed-Mode Oscillations with Multiple Time Scales
- A Geometric Model for Mixed-Mode Oscillations in a Chemical System
- Non-standard analysis and singular perturbations of ordinary differential equations
- Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
- Singular Hopf Bifurcation to Relaxation Oscillations. II
- Circle Maps and the Devil's Staircase in a Periodically Perturbed Oregonator
- Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system
- Stochastic mixed-mode oscillations in a three-species predator-prey model
- Experimental and Numerical Observation of Successive Mixed-Mode Oscillation-Incrementing Bifurcations in an Extended Bonhoeffer–van der Pol Oscillator
- Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons
- Singular Hopf Bifurcation to Relaxation Oscillations
- Mixed-mode oscillation-incrementing bifurcations and a devil’s staircase from a nonautonomous, constrained Bonhoeffer–van der Pol oscillator
- Piecewise-linear Bonhoeffer–van der Pol dynamics explaining mixed-mode oscillation-incrementing bifurcations
- Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System
