5,967 research outputs found
Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
A Langevin equation whose deterministic part undergoes a saddle-node
bifurcation is investigated theoretically. It is found that statistical
properties of relaxation trajectories in this system exhibit divergent
behaviors near a saddle-node bifurcation point in the weak-noise limit, while
the final value of the deterministic solution changes discontinuously at the
point. A systematic formulation for analyzing a path probability measure is
constructed on the basis of a singular perturbation method. In this
formulation, the critical nature turns out to originate from the neutrality of
exiting time from a saddle-point. The theoretical calculation explains results
of numerical simulations.Comment: 18pages, 17figures.The version 2, in which minor errors have been
fixed, will be published in Phys. Rev.
Bifurcation analysis of the Topp model
In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao
Traveling pulse solutions in a three-component FitzHugh-Nagumo Model
We use geometric singular perturbation techniques combined with an action
functional approach to study traveling pulse solutions in a three-component
FitzHugh--Nagumo model. First, we derive the profile of traveling -pulse
solutions with undetermined width and propagating speed. Next, we compute the
associated action functional for this profile from which we derive the
conditions for existence and a saddle-node bifurcation as the zeros of the
action functional and its derivatives. We obtain the same conditions by using a
different analytical approach that exploits the singular limit of the problem.
We also apply this methodology of the action functional to the problem for
traveling -pulse solutions and derive the explicit conditions for existence
and a saddle-node bifurcation. From these we deduce a necessary condition for
the existence of traveling -pulse solutions. We end this article with a
discussion related to Hopf bifurcations near the saddle-node bifurcation
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