The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as...The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.展开更多
Canard explosion is a kind of complex temporal behavior and is ubiquitous in excitable systems. It is associated with an abrupt change of amplitude and period of an oscillatory trajectory in a very narrow interval of ...Canard explosion is a kind of complex temporal behavior and is ubiquitous in excitable systems. It is associated with an abrupt change of amplitude and period of an oscillatory trajectory in a very narrow interval of a control parameter. We have analyzed in the present paper the behavior of canard explosion that is near a supercritical Hopf bifurcation and its response to white noise in a temporal model of CO oxidation on platinum surface. We have found that the presence of canard explosion gives rise to internal signal stochastic bi-resonance, thus demonstrating a novel functional feature of noise: selective amplifying signals with different periods.展开更多
文摘The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 20203017 & 20433050)the Foundation for the Author of National Excellent Doctorial Dissertation of China (FANEDD).
文摘Canard explosion is a kind of complex temporal behavior and is ubiquitous in excitable systems. It is associated with an abrupt change of amplitude and period of an oscillatory trajectory in a very narrow interval of a control parameter. We have analyzed in the present paper the behavior of canard explosion that is near a supercritical Hopf bifurcation and its response to white noise in a temporal model of CO oxidation on platinum surface. We have found that the presence of canard explosion gives rise to internal signal stochastic bi-resonance, thus demonstrating a novel functional feature of noise: selective amplifying signals with different periods.
