Results 251 to 260 of about 97,564 (280)

A degenerate planar piecewise linear differential system with three zones

Journal of Differential Equations, 2021
Consider the following continuous piecewise linear system defined in three zones: \[ \frac{d x}{d t}=F(x)-y, \quad \frac{d y}{d t}=g(x)-\alpha, \] where \begin{align*} F(x) & = \begin{cases} t_r (x-1)+t_c, & \text{if } x>1, \\ t_c x, & \text{if } -1\leq x \leq 1, \\ t_l (x+1)-t_c, & \text{if } x1, \\ d_c x, & \text{if } -1\leq x \leq 1, \\ d_l (x+1 ...
Hebai Chen, Man Jia, Yilei Tang
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Global Analysis of an Asymmetric Continuous Piecewise Linear Differential System with Three Linear Zones

International Journal of Bifurcation and Chaos, 2021
In [Chen et al., 2020], the third author and other coauthors studied global dynamics of the following system: [Formula: see text] in the parameter region [Formula: see text]. To study completely the piecewise linear system, we consider the parameter region [Formula: see text] in this paper.
Jiao Pu, Xiaofeng Chen, Hebai Chen, Yong-Hui Xia   +3 more
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Periodic solutions in systems of piecewise- linear differential equations

Dynamics and Stability of Systems, 1995
Motivated by the periodic behaviour of regulatory networks within cell biology and neurology, we have studied the periodic solutions of piecewise-linear, first- order differential equations with identical relative decay rates. The flow of the solution trajectories can be represented qualitatively by a directed graph.
Thomas Mestl, Erik Plahte, Stig W. Omholt   +2 more
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Limit cycles for planar piecewise linear differential systems via first integrals

Qualitative Theory of Dynamical Systems, 2002
Using first integrals, the authors provide an alternative way to the Poincaré map in order to study the limit cycles of piecewise linear differential systems. As an application of the method developed here, the authors show that a usual relaxation oscillation phenomenon occurs in a two-parameter family of planar piecewise linear vector fields.
Llibre, Jaume, Nuñez, Eduardo, Teruel, Antonio E.   +2 more
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Global dynamics of an asymmetry piecewise linear differential system: Theory and applications

Bulletin des Sciences Mathématiques, 2020
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Chen, Hebai, Wei, Fengying, Xia, Yong-Hui, Xiao, Dongmei   +3 more
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Exponentially Dichotomous Linear systems of Differential Equations with Piecewise Constant Argument

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2012
In this chapter we continue to consider differential equations with piecewise constant argument of generalized type. New elaborated results which concern, first of all, linear systems of differential equations are under discussion. An exceptional attention to the exponential dichotomy is given at the first time in literature in the paper Akhmet ...
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Chaos in a four-variable piecewise-linear system of differential equations

IEEE Transactions on Circuits and Systems, 1988
A set of four piecewise-linear ordinary differential equations in four variables is examined. The system has a single positive Lyapunov characteristic exponent. Over a parameter range, however, the Kaplan-Yorke dimension is greater than three, and the Poincare section appears to have two continuous directions.
J.L. Hudson, O.E. Rossler, H.C. Killory
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On the fold-Hopf bifurcation for continuous piecewise linear differential systems with symmetry

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010
In this paper a partial unfolding for an analog to the fold-Hopf bifurcation in three-dimensional symmetric piecewise linear differential systems is obtained. A particular biparametric family of such systems is studied starting from a very degenerate configuration of nonhyperbolic periodic orbits and looking for the possible bifurcation of limit cycles.
Llibre, Jaume, Ponce, Enrique, Ros, Javier, Torres, Francisco   +3 more
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Limit Cycles in Planar Piecewise Linear Differential Systems with Multiple Switching Curves

Qualitative Theory of Dynamical Systems
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Jia, Ranran, Zhao, Liqin
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