In this paper, we study the bifurcation of limit cycles in Liénard systems of the form dx dt = y − F (x) , dy dt = −x , where F (x) is an odd polynomial that contains, in general, several free parameters. By using a method introduced in a previous paper, we obtain a sequence of algebraic approximations to the bifurcation sets, in the parameter space. Each algebraic approximation represents an e...

In this paper we study the qualitative behavior of a predator–prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the socalled “paradox of enrich...

We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form w...

In this note, we consider Hopf bifurcation control for an Internet congestion model with a single route accessed by a single source. It has been shown that the system without control cannot guarantee a stationary sending rate. As the positive gain parameter of the system passes a critical point, Hopf bifurcation occurs. To control the Hopf bifurcation, a time-delayed feedback controller using p...

We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in...

In this paper we study the delay differential equation ẋ(t)= (a(t)x(t)+ f (t, x(t − 1))), where is a real parameter, the functions a(t), f (t, ) are C4-smooth and periodic in the variable t with period 1. Varying the parameter, eigenvalues of the monodromy operator (the derivative of the time-one map at the equilibrium 0) cross the unit circle and bifurcation of an invariant curve occurs. To de...

Percutaneous coronary intervention (PCI) for coronary bifurcation lesions has been associated with lower procedural success rates and worse clinical outcomes compared with PCI for simple coronary lesions. Angiographic evaluation alone is sometimes inaccurate and does not reflect the functional significance of bifurcation lesions. The fractional flow reserve (FFR) is an easily obtainable, reliab...

Voltage collapse and blackout can occur in an electric power system when load powers vary so that the system loses stability in a saddle node bifurcation. We propose new iterative and direct methods to compute load powers a t which bifurcation occurs and which are locally closest to the current operating load powers. The distance in load power parameter space to this locally closest bifurcation...

Non-existence and uniqueness results are proved for several local and non-local supercritical bifurcation problems involving a semilinear elliptic equation depending on a parameter. The domain is star-shaped and such that a Poincaré inequality holds but no other symmetry assumption is required. Uniqueness holds when the bifurcation parameter is in a certain range. Our approach can be seen, in s...

MOTIVATION Biochemical networks often yield interesting behavior such as switching, oscillation and chaotic dynamics. This article describes a tool that is capable of searching for bifurcation points in arbitrary ODE-based reaction networks by directing the user to regions in the parameter space, where such interesting dynamical behavior can be observed. RESULTS We have implemented a genetic ...