This paper describes the use of sums-of-square (SOS) program to compute a resilience measure for nonnegative dynamical systems. Such measure is defined as the distance between system’s nominal parameter and the closest critical paramater at which a bifurcation occur. Our proposed method uses a modeling formalism from chemical reaction network theory to describe the dynamics of nonnegative syste...

This paper deals with bifurcation analyses in current programmed DC/DC Boost converter and exhibition of chaotic behavior. This phenomenon occurs due to variation of a set of the studied circuit parameters (input voltage and a reference current). Two different types of bifurcation paths have been observed as part as part of another bifurcation arising from variation of suitable chosen parameter...

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out. Keywords—Nicholson,s blowflies model; Stability; Hopf bifurcation; Delay.

We study semilinear elliptic equations on general bounded domains with concave semipositone nonlinearities. We prove the existence of the maximal solutions, and describe the global bifurcation diagrams. When a parameter is small, we obtain the exact global bifurcation diagram. We also discuss the related symmetry breaking bifurcation when the domains have certain symmetries.

It is proved that a symmetry-breaking bifurcation occurs at a simple eigenvalue despite the usual transversality condition fails, and this bifurcation from a degenerate simple eigenvalue result complements the classical one with the transversality condition. The new result is applied to an imperfect pitchfork bifurcation, in which a forward transcritical bifurcation changes to a backward one wh...

In this article, we study the bifurcation of positive solutions for the one-dimensional (p, q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we prove the existence of multiple positive solutions and show the uniqueness of positive solutions for a...

We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the normal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determin...

In this paper, a nonlinear business cycle model of Kaldor-type with delay is considered. A Hopf bifurcation is proved to occur as the delay (taken as a parameter of bifurcation) crosses some critical value. Mathematics Subject Classification: 34K18, 91B62

We study the bifurcation loci of quadratic (and unicritical) polynomials and exponential maps. We outline a proof that the exponential bifurcation locus is connected; this is an analog to Douady and Hubbard’s celebrated theorem that (the boundary of) the Mandelbrot set is connected. For these parameter spaces, a fundamental conjecture is that hyperbolic dynamics is dense. For quadratic polynomi...

An important task for the understanding of the dynamics of parameterized systems of autonomous ordinary differential equations is the determination of the organizing centres as well as the bifurcations they exhibit (see, e.g. [Guckenheimer & Holmes, 1983; Kuznetsov, 1995; Nayfeh & Balachandran, 1995; Wiggins, 1996] as general references). The combination of analytical and numerical tools is usu...