A Theoretical Framework for Lagrangian Descriptors [PDF]
, 2017 This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigourous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs.
Balibrea-Iniesta, Francisco +4 more
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Strong Uniform Attractors for Non-Autonomous Dissipative PDEs with non translation-compact external forces [PDF]
, 2014 We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact.
Zelik, Sergey
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Transport in Transitory Dynamical Systems [PDF]
, 2010 We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.
B. A. Mosovsky, J. D. Meiss, Kaper T. J.
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Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit [PDF]
, 2006 We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a ...
A. Venkatesan +11 more
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Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction [PDF]
, 2007 We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers.
Bernardo Sánchez-rey B +3 more
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Characterizations of safety in hybrid inclusions via barrier functions [PDF]
, 2019 This paper investigates characterizations of safety in terms of barrier functions for hybrid systems modeled by hybrid inclusions. After introducing an adequate definition of safety for hybrid inclusions, sufficient conditions using continuously ...
Persidskii K. P. +3 more
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Time-Dependent Attractor for the Oscillon Equation [PDF]
, 2010 We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of arbitrary polynomial ...
Di Plinio, Francesco +2 more
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Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit [PDF]
, 2011 We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative with respect to the "time" variable corresponding to the axis of the ...
Vishik, Mark I., Zelik, Sergey V.
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Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion [PDF]
, 2015 In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the ...
Kuznetsov, N. V. +2 more
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Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems [PDF]
, 2016 In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian ...
Balibrea-Iniesta, Francisco +3 more
core +3 more sources