Invasion Waves in a Higher-Dimensional Lattice Competitive System with Stage Structure

2020 ◽  
Vol 43 (5) ◽  
pp. 3711-3723
Author(s):  
Kun Li
Keyword(s):  
Stage Structure ◽  
Competitive System ◽  
Dimensional Lattice ◽  
Higher Dimensional ◽  
Invasion Waves

scholarly journals Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Yuanke Li
Keyword(s):  
Global Stability ◽  
Toxic Effect ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Competitive System ◽  
Comparison Arguments ◽  
Double Time

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities

2021 ◽  
Vol 71 (6) ◽  
pp. 1459-1470
Author(s):  
Kun Li ◽  
Yanli He
Keyword(s):  
Traveling Wave ◽  
Solution Method ◽  
Traveling Wave Solutions ◽  
Lower Solution ◽  
Cooperative System ◽  
Lattice Systems ◽  
Dimensional Lattice ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Lower Solution Method

Abstract In this paper, we are concerned with the existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities. By using the upper and lower solution method and Schauder’s fixed point theorem, we establish the existence of traveling wave solutions. To illustrate our results, the existence of traveling wave solutions for a nonlocal delayed higher-dimensional lattice cooperative system with two species are considered.

scholarly journals WILSON LOOPS IN 2D YANG-MILLS: EULER CHARACTERS AND LOOP EQUATIONS

1996 ◽  
Vol 11 (21) ◽  
pp. 3885-3933 ◽  
Author(s):  
SANJAYE RAMGOOLAM
Keyword(s):  
Lattice Models ◽  
Symmetric Groups ◽  
Linear Constraints ◽  
Partition Functions ◽  
Wilson Loops ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Branched Covering ◽  
Large N ◽  
Higher Dimensional

We give a simple diagrammatic algorithm for writing the chiral large N expansion of intersecting Wilson loops in 2D SU(N) and U(N) Yang-Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of branched covering maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral YM 2 partition functions. We briefly discuss finite N, the nonchiral expansion, and higher-dimensional lattice models.

scholarly journals Higher dimensional lattice paths with diagonal steps

1976 ◽  
Vol 15 (2) ◽  
pp. 137-140 ◽  
Author(s):  
B.R. Handa ◽  
S.G. Mohanty
Keyword(s):  
Lattice Paths ◽  
Dimensional Lattice ◽  
Higher Dimensional
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