Traveling waves in a simple population model involving growth and death

1980 ◽  
Vol 42 (3) ◽  
pp. 397-429 ◽  
Author(s):  
C. R. Kennedy ◽  
R. Aris
Keyword(s):  
Traveling Waves ◽  
Population Model

Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice

2016 ◽  
Vol 26 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Cui-Ping Cheng ◽  
Wan-Tong Li ◽  
Zhi-Cheng Wang ◽  
Shenzhou Zheng
Keyword(s):  
Periodic Orbit ◽  
Traveling Waves ◽  
Population Model ◽  
Traveling Wave Solution ◽  
Heteroclinic Orbits ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Perturbation Problem ◽  
Spatial Lattice ◽  
Delayed Population Model

This paper is concerned with the existence of fast traveling waves connecting an equilibrium and a periodic orbit in a delayed population model with stage structure on a two-dimensional spatial lattice, under the assumption that the corresponding ODEs have heteroclinic orbits connecting an equilibrium point and a periodic solution. In this work, we rewrite the mixed functional differential equation as an integral equation in a Banach space and analyze the corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by using the Liapunov–Schmidt method and implicit function theorem.

Monotone traveling waves of a population model with non-monotone terms

2013 ◽  
Vol 219 (15) ◽  
pp. 7973-7981
Author(s):  
Zhi-Xian Yu ◽  
Ziheng Zhang ◽  
Jing Xia
Keyword(s):  
Traveling Waves ◽  
Population Model

Traveling waves in a nonlocal, piecewise linear reaction–diffusion population model

Nonlinearity ◽  
2017 ◽  
Vol 30 (8) ◽  
pp. 3304-3331 ◽  
Author(s):  
E A Autry ◽  
A Bayliss ◽  
V A Volpert
Keyword(s):  
Traveling Waves ◽  
Population Model ◽  
Piecewise Linear ◽  
Reaction Diffusion ◽  
Linear Reaction

scholarly journals Travelling waves solution for fractional-order biological population model

2021 ◽  
Vol 16 ◽  
pp. 32
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
J.F. Gómez-Aguilar ◽  
Shoaib ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Order ◽  
Traveling Waves ◽  
Population Model ◽  
Travelling Waves ◽  
Order Problem ◽  
Physical Behavior ◽  
Biological Population ◽  
The Given

In this paper, we implemented the generalized (G′/G) and extended (G′/G) methods to solve fractional-order biological population models. The fractional-order derivatives are represented by the Caputo operator. The solutions of some illustrative examples are presented to show the validity of the proposed method. First, the transformation is used to reduce the given problem into ordinary differential equations. The ordinary differential equation is than solve by using modified (G′/G) method. Different families of traveling waves solutions are constructed to explain the different physical behavior of the targeted problems. Three important solutions, hyperbolic, rational and periodic, are investigated by using the proposed techniques. The obtained solutions within different classes have provided effective information about the targeted physical procedures. In conclusion, the present techniques are considered the best tools to analyze different families of solutions for any fractional-order problem.

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