Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

2003 ◽  
Vol 76 (17) ◽  
pp. 1685-1698 ◽  
Author(s):  
Alexander V. Roup ◽  
Dennis S. Bernstein ◽  
Sergey G. Nersesov ◽  
Wassim M. Haddad ◽  
VijaySekhar Chellaboina
Keyword(s):  
Differential Equations ◽  
Limit Cycle ◽  
Impulsive Differential Equations ◽  
Poincaré Maps ◽  
Poincare Maps

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

Simplicial approximation of Poincaré maps of differential equations

1987 ◽  
Vol 124 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Frank Varosi ◽  
Celso Grebogi ◽  
James A Yorke
Keyword(s):  
Differential Equations ◽  
Poincaré Maps ◽  
Simplicial Approximation ◽  
Poincare Maps

Poincaré Maps of “ <”-Shape Planar Piecewise Linear Dynamical Systems with a Saddle

2019 ◽  
Vol 29 (12) ◽  
pp. 1950165
Author(s):  
Qianqian Zhao ◽  
Jiang Yu
Keyword(s):  
Dynamical Systems ◽  
Lower Bound ◽  
Normal Form ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Inflection Point ◽  
Piecewise Linear ◽  
Poincaré Maps ◽  
Linear Dynamical Systems ◽  
Poincare Maps

It is important in the study of limit cycles to investigate the properties of Poincaré maps of discontinuous dynamical systems. In this paper, we focus on a class of planar piecewise linear dynamical systems with “[Formula: see text]”-shape regions and prove that the Poincaré map of a subsystem with a saddle has at most one inflection point which can be reached. Furthermore, we show that one class of such systems with a saddle-center has at least three limit cycles; a class of such systems with saddle and center in the normal form has at most one limit cycle which can be reached; and a class of such systems with saddle and center at the origin has at most three limit cycles with a lower bound of two. We try to reveal the reasons for the increase of the number of limit cycles when the discontinuity happens to a system.

scholarly journals Diagnosis of a ferroresonance type through visualisation

2019 ◽  
Vol 28 ◽  
pp. 01039
Author(s):  
Łukasz Majka ◽  
Maciej Klimas
Keyword(s):  
Differential Equations ◽  
Phase Plane ◽  
Nonlinear Differential Equations ◽  
Visual Display ◽  
Time Dependent ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Test Circuit ◽  
Plane Space ◽  
Time Dependent System

The paper is focused on presenting the possible enhancements in visualisation of the ferroresonance phenomenon. The investigations have been performed with the usage of overcurrent/overvoltage responses of a ferroresonance circuit. The waveforms have been measured and recorded in a ferroresonant test circuit. Phase–plane/–space graphs analysed in this paper are a visual display of certain type characteristics for the time dependent system of nonlinear differential equations. The application of Poincare maps is also mentioned in the paper.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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