Results 91 to 100 of about 8,908 (255)

On the homoclinic orbits of the generalized Liénard equations

Applied Mathematics Letters, 2007
AbstractIn this work we study the existence of homoclinic orbits of the planar system of Liénard type ẋ=1a(x)[h(y)−F(x)],ẏ=−a(x)g(x), where a(x)>0, for every x∈R, and h is strictly increasing, but it is not assumed that h(±∞)=±∞, h(y)≤my, or h(y)≥my. We present sufficient and necessary conditions for this system to have a positive orbit which starts ...
Asadollah Aghajani, Amir Moradifam
openaire   +2 more sources

Structural obstruction to the simplicity of the eigenvalue zero in chemical reaction networks

Mathematical Methods in the Applied Sciences, Volume 47, Issue 4, Page 2993-3006, 15 March 2024.
Multistationarity is the property of a system to exhibit two distinct equilibria (steady‐states) under otherwise identical conditions, and it is a phenomenon of recognized importance for biochemical systems. Multistationarity may appear in the parameter space as a consequence of saddle‐node bifurcations, which necessarily require an algebraically ...
Nicola Vassena
wiley   +1 more source

Homoclinic orbit solutions of a one Dimensional Wilson-Cowan type model

Electronic Journal of Differential Equations, 2008
We analyze a time independent integral equation defined on a spatially extended domain which arises in the modelling of neuronal networks. In this paper, the coupling function is oscillatory and the firing rate is a smooth "heaviside-like" function ...
Edward P. Krisner
doaj  

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

, 1996
We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to ...
Aizawa Y, Arnold V I, Azuma T, Bicak J, Biesiada M, Bombelli L, Cerjan C, Charlier C L, Contopoulos G, Contopoulos G, Curzon H E J, D Hobill, Dettmann C P, Eckhardt B, Karas V, Kei-ichi Maeda, Kramar D, Maeda K, Misner C W, Moeckel R, Ong C P, Press W, Rugh S E, Shimada I, Shingo Suzuki, Sota Y, Szydlowski M, Toda M, Varvoglis H, Wiggins S, Yasuhide Sota, Zipoy M   +31 more
core   +1 more source

Oscillations in three‐reaction quadratic mass‐action systems

Studies in Applied Mathematics, Volume 152, Issue 1, Page 249-278, January 2024.
Abstract It is known that rank‐two bimolecular mass‐action systems do not admit limit cycles. With a view to understanding which small mass‐action systems admit oscillation, in this paper we study rank‐two networks with bimolecular source complexes but allow target complexes with higher molecularities.
Murad Banaji, Balázs Boros, Josef Hofbauer   +2 more
wiley   +1 more source

Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

, 2018
We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator".
Bakhanova, Yu. V., Kazakov, A. O., Korotkov, A. G., Levanova, T. A., Osipov, G. V.   +4 more
core   +1 more source

Korteweg–de Vries waves in peridynamical media

Studies in Applied Mathematics, Volume 152, Issue 1, Page 376-403, January 2024.
Abstract We consider a one‐dimensional peridynamical medium and show the existence of solitary waves with small amplitudes and long wavelength. Our proof uses nonlinear Bochner integral operators and characterizes their asymptotic properties in a singular scaling limit.
Michael Herrmann, Katia Kleine
wiley   +1 more source

Partial Hyperbolicity and Homoclinic Tangencies [PDF]

, 2011
We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic ...
Crovisier, Sylvain, Sambarino, Martin, Yang, Dawei   +2 more
core   +1 more source

Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps

, 2017
We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon maps with ...
Gonchenko, Marina, Gonchenko, Sergey V., Ovsyannikov, Ivan   +2 more
core   +1 more source

Homoclinic orbits for flows in R3

Journal de Physique, 1984
We propose a rough classification for volume contracting flows in R 3 with chaotic behaviour. In the simplest cases, one looks at the nature of a homoclinic loop for the flow. Most configurations have been studied at length in the literature; here we examine briefly the « forgotten » case.
openaire   +3 more sources