Results 61 to 70 of about 401 (174)
Homoclinic and heteroclinic bifurcations of Vector fields
Japan Journal of Applied Mathematics, 1988 The author studies a bifurcation of homoclinic and heteroclinic orbits in a k-parameter family of \((m+n)\)-dimensional ODES: \(\dot x=f(x)+g(x,\mu)\), \(x\in {\mathbb{R}}^{m+n}\), \(\mu \in {\mathbb{R}}^ k\) (k\(\geq 2)\), where f and g are smooth and \(g(x,0)=0\). Suppose that the system has three saddle equilibria \(0_ i(\mu)\), \(i=1,2,3\), and the
openaire +3 more sources
Stability of N‐front and N‐back solutions in the Barkley model
GAMM-Mitteilungen, Volume 48, Issue 1, March 2025.ABSTRACT In this article, we establish for an intermediate Reynolds number domain the stability of N$$ N $$‐front and N$$ N $$‐back solutions for each N>1$$ N>1 $$ corresponding to traveling waves, in an experimentally validated model for the transition to turbulence in pipe flow proposed in [Barkley et al., Nature 526(7574):550‐553, 2015]. We base our
Christian Kuehn, Pascal Sedlmeier
wiley +1 more source
Bifurcations of heteroclinic loops with nonresonant eigenvalues
Journal of Mathematics and Computer Science, 2017 Summary: In this paper, we use the way of local coordinates instead of the Floquet method to study the problems of homoclinic and periodic orbits bifurcated from heteroclinic loop for high-dimensional system. Under some transversal conditions and the non-twisted or twisted conditions, we discuss the existence, uniqueness, coexistence, and non ...
Guo, Zheng +3 more
openaire +2 more sources
Bifurcation diagrams for singularly perturbed system
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We consider a singularly perturbed system where the fast dynamic of the unperturbed problem exhibits a trajectory homoclinic to a critical point.
Matteo Franca
doaj +1 more source
A Multiparameter Singular Perturbation Analysis of the Robertson Model
Studies in Applied Mathematics, Volume 154, Issue 2, February 2025.ABSTRACT The Robertson model describing a chemical reaction involving three reactants is one of the classical examples of stiffness in ODEs. The stiffness is caused by the occurrence of three reaction rates k1,k2,${k}_{1},{k}_{2},$ and k3,${k}_{3},$ with largely differing orders of magnitude, acting as parameters.
Lukas Baumgartner, Peter Szmolyan
wiley +1 more source
Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities
Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 804-838, 15 January 2025.In this paper, we propose a Leslie–Gower predator–prey model in which the predator can only be captured when its population size exceeds a critical value; the mean growth rate of the prey in the absence of the predator is subject to a semi‐saturation rate that affects its birth curve, and the interaction between the two species is defined by a Holling ...
Christian Cortés García
wiley +1 more source
AIP Advances, 2020 In the present analysis, the effects of an asymmetric peristaltic movement on the bifurcations of stagnation points have been investigated. An exact analytic solution for a flow of an incompressible micropolar fluid has been established under long ...
Nasir Ali, Kaleem Ullah
doaj +1 more source
Stability of Standing Periodic Waves in the Massive Thirring Model
Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.ABSTRACT We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum.
Shikun Cui, Dmitry E. Pelinovsky
wiley +1 more source
Bifurcation diagrams for singularly perturbed system: the multi-dimensional case.
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We consider a singularly perturbed system where the fast dynamics of the unperturbed problem exhibits a trajectory homoclinic to a critical point. We assume that the slow time system admits a unique critical point, which undergoes a bifurcation as a ...
Matteo Franca
doaj +1 more source
Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative
Complexity, Volume 2025, Issue 1, 2025.This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications.
Rowshon Ara +2 more
wiley +1 more source