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Homogeneous systems of higher-order ordinary differential equations

Mike Crampin (2010)

Communications in Mathematics

The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation...

Homogeneous Systems with a Quiescent Phase

K. P. Hadeler (2008)

Mathematical Modelling of Natural Phenomena

Recently the effect of a quiescent phase (or dormant/resting phase in applications) on the dynamics of a system of differential equations has been investigated, in particular with respect to stability properties of stationary points. It has been shown that there is a general phenomenon of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower dynamics. We show that...

Homogenization of codimension 1 actions of ℝ n near a compact orbit

Marcos Craizer (1994)

Annales de l'institut Fourier

Let Φ be a C ∞ ℝ n -action on an orientable ( n + 1 ) -dimensional manifold. Assume Φ has an isolated compact orbit T and let W be a small tubular neighborhood of it. By a C ∞ change of variables, we can write W = ℝ n / ℤ n × I and T = 𝕋 n × [ 0 ] , where I is some interval containing 0.In this work, we show that by a C 0 change of variables, C ∞ outside T , we can make Φ | W invariant by transformations of the type ( x , z ) → ( x + a , z ) , a ∈ ℝ n , where x ∈ ℝ n / ℤ n and z ∈ I . As a corollary one cas describe completely the dynamics of Φ in W .

Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel

M. Neamţu, L. Buliga, F. R. Horhat, D. Opriş (2010)

Mathematical Modelling of Natural Phenomena

The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and normated function k defined...

Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers

Lan Zhang, Cheng Jian Zhang (2008)

Kybernetika

A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences...

Currently displaying 3361 – 3380 of 9312