Results 11 to 20 of about 16,168 (183)
Imperfect homoclinic bifurcations [PDF]
Physical Review E, 2001 Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an ...
Glendinning, Paul +2 more
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Structurally stable homoclinic classes [PDF]
Discrete and Continuous Dynamical Systems, 2015 arXiv admin note: substantial text overlap with arXiv:1410 ...
Wen, Xiao
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Frequency spanning homoclinic families [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2003 A family of maps or flows depending on a parameter $ $ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We consider families of periodically forced Hamiltonian systems for which the appropriately scaled frequency $\bar ( )$ is
Arnold +21 more
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Noisy homoclinic pulse dynamics [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016 The effect of stochastic perturbations on nearly homoclinic pulse trains is considered for three model systems: a Duffing oscillator, the Lorenz-like Shimizu–Morioka model, and a co-dimension-three normal form. Using the Duffing model as an example, it is demonstrated that the main effect of noise does not originate from the neighbourhood of the fixed ...
T. S. Eaves, Neil J. Balmforth
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]
Quant BiolAbstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
europepmc +2 more sources
Homoclinic and quasi-homoclinic solutions for damped differential equations
Electronic Journal of Differential Equations, 2015 We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t,u)=0, $$ where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on
Chuan-Fang Zhang, Zhi-Qing Han
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Topics in Cognitive Science, EarlyView., 2023 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
Are physiological oscillations physiological?
The Journal of Physiology, EarlyView., 2023 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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Nonreversible homoclinic snaking [PDF]
Dynamical Systems, 2011 Homoclinic snaking refers to the sinusoidal snaking continuation curve of homoclinic orbits near a heteroclinic cycle connecting an equilibrium E and a periodic orbit P. Along this curve the homoclinic orbit performs more and more windings about the periodic orbit. Typically this behaviour appears in reversible Hamiltonian systems. Here we discuss this
Knobloch, Jürgen +2 more
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Nonhyperbolic homoclinic chaos [PDF]
Physics Letters A, 1999 Homoclinic chaos is usually examined with the hypothesis of hyperbolicity of the critical point. We consider here, following a (suitably adjusted) classical analytic method, the case of non-hyperbolic points and show that, under a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic
CICOGNA, GIAMPAOLO, Santoprete M.
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