Journal of Nonlinear Science
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Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics
Journal of Nonlinear Science - Tập 34 - Trang 1-36 - 2024
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......
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
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}}......
Markov Models of Coarsening in Two-Dimensional Foams with Edge Rupture
Journal of Nonlinear Science - - 2021
Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example
Journal of Nonlinear Science - Tập 27 - Trang 1215-1234 - 2017
Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the ......
Small-Time Extinction with Decay Estimate of Bilinear Systems on Hilbert Space
Journal of Nonlinear Science - Tập 33 - Trang 1-27 - 2023
This paper considers the stabilization problem of bilinear systems in small time by various feedback laws. Then, under some reasonable assumptions on the system and control operator, we prove the global polynomial stabilization of the bilinear system, at hand, in a small time by unbounded feedback. A decay rate of the stabilized state is explicitly estimated. Moreover, we use an observability cond......
The Rotating Rigid Body Model Based on a Non-twisting Frame
Journal of Nonlinear Science - Tập 30 - Trang 3199-3233 - 2020
This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptio......
On the Extension of Onsager’s Conjecture for General Conservation Laws
Journal of Nonlinear Science - Tập 29 - Trang 501-510 - 2018
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the “universality” of the Onsager exponent,
$$\alpha > 1/3$$
, concernin......
On Energy Cascades in the Forced 3D Navier–Stokes Equations
Journal of Nonlinear Science - Tập 26 - Trang 683-715 - 2016
We show—in the framework of physical scales and
$$(K_1,K_2)$$
-averages—that Kolmogorov’s dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier–Stokes equatio......
Hamel’s Formalism for Infinite-Dimensional Mechanical Systems
Journal of Nonlinear Science - Tập 27 - Trang 241-283 - 2016
In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinit......
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