Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive...

Abstract. A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence ...

A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the s...

The purpose of the present paper is to prove that there are nonconstant periodic integral curves of a mathematical model of cancer growth. We shall prove, there are Hopf bifurcations in the mathematical model and that the oscillating solutions are uniformly, asymptotically stable.

Two dynamical models that have been proposed for determining aspects of confined plasma behavior around L–H transitions are analysed using singular-ity theory and stability theory. The recognition problem for the unperturbed bifurcation sets is solved by applying singularity theory methods to determine the normal form and codimension of the singular points. We find that in both cases the unpert...

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive ...

We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or helical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the stability of the fixed points in this system...

The “Q-curves” Q1(c) = c,Q2(c) = c + c, . . . , Qn(c) = (Qn−1(c)) + c = f c (0) have long been observed and studied as the shadowy curves which appear illusively — not explicitly drawn — in the familiar orbit diagram of Myrberg’s map fc(x) = x + c. We illustrate that Q-curves also appear implicitly, for a different reason, in a computer-drawn bifurcation diagram of x + c as well — by “bifurcati...

We outline the theory of equivariant transversality for maps equivariant with respect to a compact Lie group. We indicate some applications to generic equivariant bifurcation theory.