scholarly journals Is there a Connection between Local and Global (In-)Stability?

1986 ◽  
Vol 39 (3) ◽  
pp. 331 ◽  
Author(s):  
B Eckhardt ◽  
JA Louw ◽  
W-H Steeb
Keyword(s):  
Stability Analysis ◽  
Hamiltonian Systems ◽  
Local Stability ◽  
Large Scale ◽  
Equations Of Motion ◽  
Riemannian Curvature ◽  
Local Stability Analysis

We review two criteria which have been used to predict the onset of large scale stochasticity in Hamiltonian systems. We show that one of them, due to Toda and based on a local stability analysis of the equations of motion, is inconclusive. An approach based on the local Riemannian curvature K of trajectories correctly predicts chaos if K < 0 everywhere, but�no further conclusions can be drawn. New (counter-)examples are provided.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

scholarly journals Dynamic Modeling and Stability Analysis of Mechanical Systems with Time-Varying Topologies

1993 ◽  
Vol 115 (4) ◽  
pp. 808-816 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Modeling ◽  
Local Stability ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Kinematic Constraints ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of a Poincare´ map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of a dynamic model and a local stability analysis are presented.

Stability and Bifurcation Analysis of a Delayed Discrete Predator–Prey Model

2018 ◽  
Vol 28 (09) ◽  
pp. 1850116 ◽  
Author(s):  
A. M. Yousef ◽  
S. M. Salman ◽  
A. A. Elsadany
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Chaotic Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Stability Analysis ◽  
Prey Model ◽  
Stability And Bifurcation Analysis ◽  
Different Types ◽  
Two Parameters

A discrete predator–prey model with delayed density dependence in the rate of growth of the prey is considered. In particular, we analyze the model presented by Kot [2005] which consists of three coupled difference equations and contains two parameters. Existence and local stability analysis of fixed points of the model are addressed. The normal form technique and perturbation method are applied to the different types of bifurcations that exist in the model being investigated. It is proved that the existence of transcritical and Neimark–Sacker bifurcations can occur in the model. In addition, the chaotic behavior of the model in the sense of Marotto is proved. To verify the results obtained analytically, we perform numerical simulations which also explore further the richer dynamics of the model.

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