1:2 Resonance Bifurcation in the E-I Map

1:2 Resonance Bifurcation in the E-I Map

Bifurcation and Continuation

The movie comprises a sequence of phase portraits of the E-I map in the vicinity of the codimension 2 point of a 1:2 resonance bifurcation occurring on a period 2 orbit as a parameter is varied.


Bifurcations without parameters

Bifurcations without parameters

Bifurcation and Simulations

 The following pictures illustrate some elements of the nonlinear dynamics near equilibrium manifolds.


Breathing torus near double Hopf bifurcation

Breathing torus near double Hopf bifurcation

Bifurcation and Continuation


Canard Explosion

Canard Explosion

Bifurcation and Simulations

Periodic orbit continuation in the Hindmarsh-Rose model: canard explosion.


Canard explosion in the FitzHugh-Nagumo model

Canard explosion in the FitzHugh-Nagumo model

Bifurcation and Continuation

This animation illustrates the phenomenon of canard explosion in the FitzHugh-Nagumo model. 


Global Saddle-Node Bifurcations in a Neuron Model

Global Saddle-Node Bifurcations in a Neuron Model

Bifurcation and Simulations

The stunning term, "Blue Sky Catastrophe" has been given to the last, out of the seven known, main bifurcations of a periodic orbit.


Hopf Bifurcations in Evolutionary Dynamics

Hopf Bifurcations in Evolutionary Dynamics

Bifurcation and Continuation


Mode-locking in Piecewise Smooth Maps

Mode-locking in Piecewise Smooth Maps

Bifurcation and Continuation

Resonance (mode-locking) tongues are commonly observed in smooth circle maps, and Neimark-Sacker bifurcations.


Topology of bursting activity in a 3D neuron model

Topology of bursting activity in a 3D neuron model

Bifurcation and Simulations

Three views on the parameterized slow motion manifolds and the 2D nullcline in a 3D leech inter-heart neuron model.


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