Results 41 to 50 of about 636 (179)
A study of chaos for processes under small perturbations II: rigorous proof of chaos [PDF]
Opuscula Mathematica, 2010 In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation \[\dot{z}=\left(1 + e^{i\kappa t} |z|^2\right)\bar{z}^2 - N e^{-i\frac{\pi}{3}}.\] Heteroclinic and homoclinic connections between two periodic solutions ...
Piotr Oprocha, Paweł Wilczyński
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Global bifurcation of homoclinic solutions of Hamiltonian systems
Discrete and Continuous Dynamical Systems, 2003 We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
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Are physiological oscillations physiological?
The Journal of Physiology, Volume 604, Issue 9, Page 3672-3693, 1 May 2026.Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
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Cross soliton and breather soliton for the (3+1) $(3+1)$-dimensional Yu–Toda–Sasa–Fukuyama equation
Advances in Difference Equations, 2019 Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach with perturbation parameter u0 $u_{0}$ and complexity of parameters, respectively.
Zhiqiang Pu, Zhigang Pan
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Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Advances in Difference Equations, 2010 The authors consider the nonlinear difference equation \[ \Delta(p(n)(\Delta u(n-1))^\delta)-q(n)(x(n))^\delta=f(n,u(n)),\quad n\in\mathbb{Z}, \] where \(\Delta\) is the usual forward difference operator, \(\delta\) is the ratio of odd positive integers, \(p,q\) are real sequences with \(p(n)\neq 0\), and \(f:\mathbb{Z}\times\mathbb{Z}\to\mathbb{R ...
Chen Peng, Tang XH
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most ...
Raffaele Folino +2 more
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Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations
Boundary Value Problems, 2009 This paper investigates the singular differential equation (p(t)u′)′=p(t)f(u), having a singularity at t=0. The existence of a strictly increasing solution (a homoclinic solution) satisfying u′(0)=0, u(∞)=L>0 is proved ...
Irena Rachůnková +1 more
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Mathematics, 2022 The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
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Periodic and Homoclinic Solutions of Extended Fisher–Kolmogorov Equations
Journal of Mathematical Analysis and Applications, 2000 The authors study the existence of periodic and homoclinic solutions to fourth-order semilinear equations via variational methods.
Tersian, Stepan, Chaparova, Julia
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer +2 more
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