Results 1 to 10 of about 633,095 (156)
Reconfiguration of a smart surface using heteroclinic connections [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017 A reconfigurable smart surface with multiple equilibria is presented, modelled using discrete point masses and linear springs with geometric nonlinearity. An energy-efficient reconfiguration scheme is then investigated to connect equal-energy unstable (but actively controlled) equilibria.
Jiaying Zhang, Colin R McInnes
exaly +10 more sources
Homo- and Heteroclinic Connections in the Planar Solar-Sail Earth-Moon Three-Body Problem [PDF]
Frontiers in Applied Mathematics and Statistics, 2018 This paper explores the existence of homo- and heteroclinic connections between solar-sail periodic orbits in the planar Earth-Moon circular restricted three-body problem.
Jeannette Heiligers
exaly +6 more sources
A Sequence of Order Relations: Encoding Heteroclinic Connections in Scalar Parabolic PDE [PDF]
Journal of Differential Equations, 2002 We address the problem of heteroclinic connections in the attractor of dissipative scalar semilinear parabolic equations ut = uxx + ƒ (x, u, ux), 0 < x < 1 on a bounded interval with Neumann conditions. Introducing a sequence of order relations, we prove a new and simple criterion for the existence of heteroclinic connections, using only ...
Wolfrum, Matthias
exaly +5 more sources
Unification of free energy minimization, spatiotemporal energy, and dimension reduction models of V1 organization: Postnatal learning on an antenatal scaffold [PDF]
Frontiers in Computational Neuroscience, 2022 Developmental selection of neurons and synapses so as to maximize pulse synchrony has recently been used to explain antenatal cortical development. Consequences of the same selection process—an application of the Free Energy Principle—are here followed ...
James Joseph Wright +2 more
doaj +2 more sources
The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations [PDF]
SIAM Journal on Applied Mathematics, 1993 Weakly nonlinear reaction-diffusion equations with gradient structure are considered, namely \(\partial u/\partial t = \partial^ 2u/\partial x^ 2 = \lambda f(u)\), \(x \in (0,1)\), \(t > 0\); \(u(0,t) = u(1,t) = 0\), \(t > 0\); \(u(x,0) = u_ 0(x)\), \(x \in [0,1]\), where the nonlinearity \(f(u)\) is an odd polynomial in \(u\) (Cahn-Hilliard equations).
Andrew Stuart +2 more
exaly +4 more sources
Heteroclinic connections for a class of non-autonomous systems
Electronic Journal of Differential Equations, 2001 We prove the existence of heteroclinic connections for a system of ordinary differential equations, with time-dependent coefficients, which is reminiscent of the ODE arising in connection with traveling waves for the Fisher equation.
L. Sanchez
doaj +2 more sources
SIAM Journal on Applied Dynamical SystemsThis paper presents a methodology for the computation of whole sets of heteroclinic connections between isoenergetic slices of center manifolds of center \times center \times saddle fixed points of autonomous Hamiltonian systems. It involves (a) computing Taylor expansions of the center-unstable and center-stable manifolds of the departing and arriving
Alex Haro, Miquel Barcelona Poza
exaly +6 more sources
Examples and Counterexamples, 2022 Using a vector field in R4, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple, quasi-simple and pseudo ...
Sofia B.S.D. Castro, Alexander Lohse
doaj +1 more source
About the Structure of Attractors for a Nonlocal Chafee-Infante Problem
Mathematics, 2021 In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem.
Rubén Caballero +3 more
doaj +1 more source
Metric methods for heteroclinic connections [PDF]
Mathematical Methods in the Applied Sciences, 2016 We consider the problem among curves connecting two given wells of W≥0, and we reduce it, following a standard method, to a geodesic problem of the form with . We then prove existence of curves minimizing this new action just by proving that the distance induced by K is proper (i.e., its closed balls are compact). The assumptions on W are minimal,
Monteil, Antonin, Santambrogio, Filippo
openaire +3 more sources