Heteroclinic orbits in singular systems: A unifying approachSpringer Science and Business Media LLC - Tập 6 - Trang 147-173 - 1994
Flaviano Battelli
We consider singularly perturbed systems
$$\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )$$
, such thatξ=f(ξ, αo, 0). αo∃ℝ
m
, has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system ha...... hiện toàn bộ
Comparison between the Deterministic and Stochastic Models of Nonlocal DiffusionSpringer Science and Business Media LLC - - Trang 1-20 - 2022
Itsuki Watanabe, Hiroshi Toyoizumi
In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference ...... hiện toàn bộ
Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin GasdynamicsSpringer Science and Business Media LLC - Tập 34 - Trang 1067-1084 - 2020
Rahul Kumar Chaturvedi, L. P. Singh, Dia Zeidan
The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine–Hugoniot relations for delta shock wave which are utilized to determine the strength, posi...... hiện toàn bộ
Dynamical Properties of Models for the Calvin CycleSpringer Science and Business Media LLC - Tập 26 - Trang 673-705 - 2014
Alan D. Rendall, Juan J. L. Velázquez
Modelling the Calvin cycle of photosynthesis leads to various systems of ordinary differential equations and reaction-diffusion equations. They differ by the choice of chemical substances included in the model, the choices of stoichiometric coefficients and chemical kinetics and whether or not diffusion is taken into account. This paper studies the long-time behaviour of solutions of several of th...... hiện toàn bộ
Normalizations with Exponentially Small Remainders for Nonautonomous Analytic Periodic Vector FieldsSpringer Science and Business Media LLC - Tập 24 - Trang 289-323 - 2012
Tiphaine Jézéquel
In this paper we deal with analytic nonautonomous vector fields with a periodic time-dependency, that we study near an equilibrium point. In a first part, we assume that the linearized system is split in two invariant subspaces E
0 and E
1. Under light diophantine conditions on the eigenvalues of the linear part, we prove that there is a polynomial change of coordin...... hiện toàn bộ
Properties of the attractor of a scalar parabolic PDESpringer Science and Business Media LLC - Tập 3 - Trang 575-591 - 1991
Carlos Rocha
We consider a general scalar one-dimensional semilinear parabolic partial differential equation generating a semiflow with an attractor in an adequate state space. Generalizing known results, it is shown that this attractor is the graph of a function over a compact subset of a finite-dimensional subspace of the state space. In addition, we construct an example with a special interest for the geome...... hiện toàn bộ
Bifurcations of Limit Cycles in a Z8-Equivariant Planar Vector Field of Degree 7Springer Science and Business Media LLC - Tập 16 - Trang 1123-1139 - 2004
Jibin Li, Mingqiang Zhang
The weakened Hilberts 16th problem for symmetric planar perturbed polynomial Hamiltonian systems is considered. An example of Z8-equivariant planar perturbed Hamiltonian systems is constructed. By using bifurcation theory of planar dynamical systems and the method of detection functions, under the help of numerical analysis, it is shown that there exist parameter groups such that this perturbed Ha...... hiện toàn bộ
The relative variance criterion for stability of delay systemsSpringer Science and Business Media LLC - Tập 5 - Trang 105-128 - 1993
Robert F. V. Anderson
A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables use...... hiện toàn bộ