Results 51 to 60 of about 10,271 (227)
Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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Bifurcation and chaos for piecewise nonlinear roll system of rolling mill
Advances in Mechanical Engineering, 2017 A non-smooth cold roll system of rolling mill is studied to reveal the bifurcation of the piecewise-smooth and discontinuous system. To examine the influence of the parameters on the dynamics, the bifurcation diagram is constructed when it is unperturbed.
Chundi Si +3 more
doaj +1 more source
The non-transverse Shil’nikov–Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies [PDF]
Physica D: Nonlinear Phenomena, 1999 The authors consider a degenerate codimension 3 Shilnikov-Hopf bifurcation when at critical values of parameters a three-dimensional smooth vector field has a singular point \(O\) with eigenvalues \((\pm i\omega\), \(\lambda>0)\) and \(O\) has a homoclinic orbit.
Champneys, AR, Rodriguez-Luis, AJ
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Topics in Cognitive Science, Volume 18, Issue 3, July 2026.Abstract Fractal fluctuations are a core concept for inquiries into human behavior and cognition from a dynamic systems perspective. Here, we present a generalized variance method for multivariate detrended fluctuation analysis (mvDFA). The advantage of this extension is that it can be applied to multivariate time series and considers intercorrelation ...
Sebastian Wallot +5 more
wiley +1 more source
Variational approximations to homoclinic snaking [PDF]
Physical Review E, 2011 4 pages, 3 figures ...
Susanto, H., Matthews, P. C.
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq +4 more
wiley +1 more source
Continuation of Homoclinic Orbits in Matlab [PDF]
, 2005 We have added the functionality for continuing homoclinic orbits to cl_matcont, a user-friendly matlab package for the study of dynamical systems and their bifurcations. It is now possible to continue homoclinic-to-hyperbolic-saddle and homoclinic-to-saddle-node orbits.
Mark J. Friedman +3 more
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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
wiley +1 more source
Variational and penalization methods for studying connecting orbits of Hamiltonian systems
Electronic Journal of Differential Equations, 2000 In this article, we consider a class of second order Hamiltonian systems that possess infinite or finite number of equilibria. Variational arguments will be used to study the existence of connecting orbits joining pairs of equilibria.
Chao-Nien Chen, Shyuh-yaur Tzeng
doaj
Invariant manifolds of homoclinic orbits: super-homoclinics and multi-pulse homoclinic loops
, 2020 Consider a Hamiltonian flow on R4 with a hyperbolic equilibrium O and a transverse homoclinic orbit Γ. In this thesis, we study the dynamics near Γ in its energy level when it leaves and enters O along strong unstable and strong stable directions, respectively. In particular, we provide necessary and sufficient conditions for the existence of the local
openaire +2 more sources