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......
Gyroscopic control and stabilization
Journal of Nonlinear Science - Tập 2 - Trang 367-415 - 1992
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......
For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification
Journal of Nonlinear Science - - 2003
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
$${\dot{x}}......
Markov Models of Coarsening in Two-Dimensional Foams with Edge Rupture
Journal of Nonlinear Science - - 2021
Analysis of Underactuated Dynamic Locomotion Systems Using Perturbation Expansion: The Twistcar Toy Example
Journal of Nonlinear Science - Tập 27 - Trang 1215-1234 - 2017
Underactuated robotic locomotion systems are commonly represented by nonholonomic constraints where in mixed systems, these constraints are also combined with momentum evolution equations. Such systems have been analyzed in the literature by exploiting symmetries and utilizing advanced geometric methods. These works typically assume that the shape variables are directly controlled, and obtain the ......
Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms
Journal of Nonlinear Science - Tập 7 - Trang 371-409 - 1997
Two related systems of coupled modulation equations are studied and compared in this paper. The modulation equations are derived for a certain class of basic systems which are subject to two distinct, interacting, destabilising mechanisms. We assume that, near criticality, the ratio of the widths of the unstable wavenumber-intervals of the two (weakly) unstable modes is small—as, for instance, can......
Small-Time Extinction with Decay Estimate of Bilinear Systems on Hilbert Space
Journal of Nonlinear Science - Tập 33 - Trang 1-27 - 2023
This paper considers the stabilization problem of bilinear systems in small time by various feedback laws. Then, under some reasonable assumptions on the system and control operator, we prove the global polynomial stabilization of the bilinear system, at hand, in a small time by unbounded feedback. A decay rate of the stabilized state is explicitly estimated. Moreover, we use an observability cond......
Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in $${\mathbb {R}}^n$$: (I) Under-Damping Case
Journal of Nonlinear Science - Tập 33 Số 1 - 2023
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......
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