where X is an appropriate function space and φi , F are given functions. The coefficients φi’s are different in general. In the particular case where φi(|ξ |)= |ξ |p−2, for all ξ ∈ R , for all i ∈ {1, . . . ,N}, (1.1) reduces to the p-Laplacian equation and there are several bifurcation results available (cf. [3, 4]). It seems that bifurcation problems for anisotropic elliptic operators have no...

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...

We derive a uniform approximation for semiclassical contributions of periodic orbits to the spectral density which is valid for generic period-quadrupling bifurcations in systems with a mixed phase space. These bifurcations involve three periodic orbits which coalesce at the bifurcation. In the vicinity of the bifurcation the three orbits give a collective contribution to the spectral density w...

In this paper, we investigate bifurcation processes for the mean eld theory (MFT) annealing applied to traveling salesman problems (TSPs). Due to the symmetries of the TSP free energy function, some special bifurcations occur: cyclic symmetry breaking bifurcations and reverse symmetry breaking bifurcations. Saddle-node bifurcations also occur. Which type of bifurcations occurs depends on the sy...

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obt...

The stability and Hopf bifurcation of the positive steady state to a general scalar reaction–diffusion equation with distributed delay and Dirichlet boundary condition are investigated in this paper. The time delay follows a Gamma distribution function. Through analyzing the corresponding eigenvalue problems, we rigorously show that Hopf bifurcations will occur when the shape parameter n ≥ 1, a...

The aim of this paper is to investigate the bifurcation and chaotic behaviour in the two-parameter family of transcendental functions fλ,n(x) = λ x (ex+1)n , λ > 0, x ∈ R, n ∈ N\{1} which arises from the generating function of the generalized Apostol-type polynomials. The existence of the real fixed points of fλ,n(x) and their stability are studied analytically and the periodic points of fλ,n(x...

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from giv...

In systems with switching actuators persistent motions of different nature may occur, such as limit cycles, quasi-periodic and chaotic motions. In this contribution the nature of persistent motions in an attitude control system with switching actuators subject to switching restrictions are examined as a function of controller parameters. Bifurcation diagrams are used to describe observations. I...

A reaction-diffusion population model with a general time-delayed growth rate per capita is considered. From a careful analysis of the characteristic equation, the stability of the positive steady state solution and the existence of supercritical Hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem, where the time delay is used as the bifurcati...