Journal of Nonlinear Science

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Modulation Theory for Radially Symmetric Kink Waves Governed by a Multi-Dimensional Sine-Gordon Equation
Journal of Nonlinear Science - Tập 33 - Trang 1-25 - 2022
Lu Trong Khiem Nguyen, Noel Frederick Smyth
We derive a modulation theory for the resolution of radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation. Whitham modulation theory is developed to explain the return of an expanding kink wave, as well as predicting its maximum expansion radius and its return time. Comparisons with full numerical solutions of the sine-Gordon equation show that the modulation theory gi...... hiện toàn bộ
Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation
Journal of Nonlinear Science - Tập 33 - Trang 1-52 - 2023
Telmo Peixe, Alexandre A. Rodrigues
This paper analyses the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a one-parameter model developed in the context of polymatrix replicator equations. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to...... hiện toàn bộ
Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics
Journal of Nonlinear Science - Tập 34 - Trang 1-36 - 2024
Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío
Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived fr...... hiện toàn bộ
Gyroscopic control and stabilization
Journal of Nonlinear Science - Tập 2 - Trang 367-415 - 1992
L. -S. Wang, P. S. Krishnaprasad
In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic systems, when the forces are determined by a suitable class of feedback laws. To assess the stability of relative equilibria in the resultant feedback systems, we extend the ene...... hiện toàn bộ
For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification
Journal of Nonlinear Science - - 2003
Eduardo D. Sontag
Poincaré’s Equations for Cosserat Media: Application to Shells
Journal of Nonlinear Science - Tập 27 - Trang 1-44 - 2016
Frederic Boyer, Federico Renda
In 1901, Henri Poincaré discovered a new set of equations for mechanics. These equations are a generalization of Lagrange’s equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we apply an extended version of these equations to ...... hiện toàn bộ
Hopf-Like Bifurcations and Asymptotic Stability in a Class of 3D Piecewise Linear Systems with Applications
Journal of Nonlinear Science - Tập 31 - Trang 1-37 - 2021
Rony Cristiano, Durval J. Tonon, Mariana Q. Velter
The main purpose of this paper is to analyze the Hopf-like bifurcations in 3D piecewise linear systems. Such bifurcations are characterized by the birth of a piecewise smooth limit cycle that bifurcates from a singular point located at the discontinuity manifold. In particular, this paper concerns systems of the form $${\dot{x}}...... hiện toàn bộ
Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination
Journal of Nonlinear Science - Tập 30 - Trang 2671-2736 - 2020
P. Degond, A. Diez, A. Frouvelle, S. Merino-Aceituno
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in $${\mathbb {R}}^3$$ as in Degond et al. (Math Models Methods Appl Sci 27(6):1005–1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribu...... hiện toàn bộ
Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems
Journal of Nonlinear Science - Tập 31 - Trang 1-38 - 2021
Li Chen, Esther S. Daus, Alexandra Holzinger, Ansgar Jüngel
Population cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. I...... hiện toàn bộ
Complex-Valued Burgers and KdV–Burgers Equations
Journal of Nonlinear Science - Tập 20 - Trang 341-360 - 2010
Netra Khanal, Jiahong Wu, Juan-Ming Yuan, Bing-Yu Zhang
Spatially periodic complex-valued solutions of the Burgers and KdV–Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial datum such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild co...... hiện toàn bộ
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