摘要
A trajectory following the repelling branch of an equilibrium or a periodic orbit is called a canards solution. Using a continuation method, we find a new type of canards bursting which manifests itseff in an alternation between the oscillation phase following attracting the limit cycle branch and resting phase following a repelling fixed point branch in a reduced leech neuron model Via periodic-chaotic alternating of infinite times, the number of windings within a canards bursting can approach infinity at a Gavrilov-Shilnikov homoclinic tangency bifurcation of a simple saddle limit cycle.
A trajectory following the repelling branch of an equilibrium or a periodic orbit is called a canards solution. Using a continuation method, we find a new type of canards bursting which manifests itseff in an alternation between the oscillation phase following attracting the limit cycle branch and resting phase following a repelling fixed point branch in a reduced leech neuron model Via periodic-chaotic alternating of infinite times, the number of windings within a canards bursting can approach infinity at a Gavrilov-Shilnikov homoclinic tangency bifurcation of a simple saddle limit cycle.
基金
Supported by Natural Science Foundation of China under Grant No 10432010.
