scholarly journals A computational framework for connection matrix theory

2021 ◽  
Author(s):  
Shaun Harker ◽  
Konstantin Mischaikow ◽  
Kelly Spendlove
Keyword(s):  
Matrix Theory ◽  
Connection Matrix ◽  
Computational Framework

A global two-dimensional version of Smale’s cancellation theorem via spectral sequences

2015 ◽  
Vol 36 (6) ◽  
pp. 1795-1838 ◽  
Author(s):  
M. A. BERTOLIM ◽  
D. V. S. LIMA ◽  
M. P. MELLO ◽  
K. A. DE REZENDE ◽  
M. R. DA SILVEIRA
Keyword(s):  
Sequence Analysis ◽  
Spectral Sequence ◽  
Matrix Theory ◽  
Chain Complex ◽  
Connection Matrix ◽  
Local Version ◽  
Two Dimensional ◽  
Dimensional Version ◽  
Cancellation Theorem ◽  
Flows On Surfaces

In this article, Conley’s connection matrix theory and a spectral sequence analysis of a filtered Morse chain complex $(C,{\rm\Delta})$ are used to study global continuation results for flows on surfaces. The briefly described unfoldings of Lyapunov graphs have been proved to be a well-suited combinatorial tool to keep track of continuations. The novelty herein is a global dynamical cancellation theorem inferred from the differentials of the spectral sequence $(E^{r},d^{r})$. The local version of this theorem relates differentials $d^{r}$ of the $r$th page $E^{r}$ to Smale’s theorem on cancellation of critical points.

scholarly journals Connection matrix theory for discrete dynamical systems

1999 ◽  
Vol 47 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Piotr Bartłomiejczyk ◽  
Zdzisław Dzedzej
Keyword(s):  
Dynamical Systems ◽  
Matrix Theory ◽  
Discrete Dynamical Systems ◽  
Connection Matrix

scholarly journals The Connection Matrix analysis of a Prey-Predator system with a Strong Allee effect and multiple interior equilibria

2021 ◽  
Author(s):  
Asim Sikder
Keyword(s):  
Functional Response ◽  
Death Rate ◽  
Allee Effect ◽  
Matrix Theory ◽  
Matrix Analysis ◽  
Connection Matrix ◽  
Connecting Orbits ◽  
Strong Allee Effect ◽  
Predator System ◽  
Robust Permanence

Abstract We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.

Modification of Tatsuoka’s Q Matrix Theory

2009 ◽  
Vol 41 (2) ◽  
pp. 175-181 ◽  
Author(s):  
Shu-Liang DING ◽  
Yu-Fang ZHU ◽  
Hai-Jing LIN ◽  
Yan CAI
Keyword(s):  
Matrix Theory
Sign in / Sign up

Export Citation Format

Share Document