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Bifurcations on a Five-Parameter Family of Planar Vector Field
Springer Science and Business Media LLC - Tập 20 - Trang 961-980 - 2008
In this paper we consider a five-parameter family of planar vector fields
$${X_{\mu}: \, \begin{array}{ll} \frac{dx}{dt} = y,\\ \frac{dy}{dt} = x^4+\mu_3x^2+\mu_2x+\mu_1 +y(\mu_4+\mu_5x\\ \quad+\,c(\mu )x^2+x^3h(x,\mu))+y^2Q(x,y,\mu), \end{array}}$$
where μ = (μ
1, μ
...... hiện toàn bộ
Linear Stability of Traveling Waves in First-Order Hyperbolic PDEs
Springer Science and Business Media LLC - Tập 23 - Trang 365-393 - 2011
In the analysis of traveling waves it is common that coupled parabolic-hyperbolic problems occur, where the hyperbolic part is not strictly hyperbolic. For example, this happens whenever a reaction diffusion equation with more than one non-diffusing component is considered in a co-moving frame. In this paper we analyze the stability of traveling waves in nonstrictly hyperbolic PDEs by reformulatin...... hiện toàn bộ
Intra- and Inter-Specific Competitions of Two Stage-Structured Species in a Patchy Environment
Springer Science and Business Media LLC -
Bendixson-Dulac Criteria for Difference Equations
Springer Science and Business Media LLC - Tập 10 - Trang 567-575 - 1998
Conditions are given which preclude the existence of a nontrivial periodic orbit for a difference equation in ℝn. The conditions are analogous to those of Bendixson and Dulac for autonomous planar differential equations.
Floquet’s Theorem and Stability of Periodic Solitary Waves
Springer Science and Business Media LLC - Tập 21 - Trang 555-565 - 2009
This paper is concerned with the spectrum the Hill operator L(y) = −y′′ + Q(x) y in
$${L^{2}_{\rm per}[0, \pi]}$$
. We show that the eigenvalues of L can be characterized by knowing one of its eigenfunctions. Applications are given to nonlinear stability of a class of periodic problems.
On the Dynamics of Mechanical Systems with the Homogeneous Polynomial Potential V = ax 4 + cx 2 y 2
Springer Science and Business Media LLC - Tập 21 - Trang 527-554 - 2009
This paper is devoted to analyze certain dynamical aspects of the planar mechanical system associated to the potential V = ax
4 + cx
2
y
2 as a function of the real parameters a and c.
Asymptotic Properties of a Stochastic SIR Epidemic Model with Beddington–DeAngelis Incidence Rate
Springer Science and Business Media LLC - Tập 30 - Trang 93-106 - 2017
In this paper, the stochastic SIR epidemic model with Beddington–DeAngelis incidence rate is investigated. We classify the model by introducing a threshold value
$$\lambda $$
. To be more specific, we show that if
...... hiện toàn bộ
Chain recurrence, semiflows, and gradients
Springer Science and Business Media LLC - Tập 7 - Trang 437-456 - 1995
This paper is a study of chain recurrence and attractors for maps and semiflows on arbitrary metric spaces. The main results are as follows. (i) C. Conley's characterization of chain recurrence in terms of attractors holds for maps and semiflows on any metric space. (ii) An alternative definition of chain recurrence for semiflows is given and is shown to be equivalent to the usual definition. The ...... hiện toàn bộ
Analysis of Newton’s Method to Compute Travelling Waves in Discrete Media
Springer Science and Business Media LLC - Tập 17 - Trang 523-572 - 2005
We present a variant of Newton’s method for computing travelling wave solutions to scalar bistable lattice differential equations. We prove that the method converges to a solution, obtain existence and uniqueness of solutions to such equations with a small second order term and study the limiting behaviour of such solutions as this second order term tends to zero. The robustness of the algorithm w...... hiện toàn bộ
A Topological Proof of Stability of N-Front Solutions of the FitzHugh–Nagumo Equations
Springer Science and Business Media LLC - Tập 11 - Trang 515-555 - 1999
Consideration is devoted to traveling N-front wave solutions of the FitzHugh–Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to d...... hiện toàn bộ
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