# Competition in periodic media: I -- Existence of pulsating fronts

@article{Girardin2016CompetitionIP, title={Competition in periodic media: I -- Existence of pulsating fronts}, author={L{\'e}o Girardin}, journal={arXiv: Analysis of PDEs}, year={2016} }

This paper is concerned with the existence of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. Considering highly competitive systems, a simple "high frequency or small amplitudes" algebraic sufficient condition for the existence of pulsating fronts is stated. This condition is in fact sufficient to guarantee that all periodic coexistence states vanish and become unstable as the competition becomes large enough.

#### 9 Citations

Competition in Periodic Media: III—Existence and Stability of Segregated Periodic Coexistence States

- Mathematics
- 2018

Competition in periodic media: II -- Segregative limit of pulsating fronts and "Unity is not Strength"-type result

- Mathematics
- 2016

Pulsating fronts and front-like entire solutions for a reaction–advection–diffusion competition model in a periodic habitat

- Mathematics
- 2019

Equilibria and stability issues for diffusive Lotka-Volterra system in a heterogeneous setting for large diffusivities

- Mathematics
- 2017

The effect of random dispersal on competitive exclusion - A review.

- Economics, Medicine
- Mathematical biosciences
- 2019

#### References

SHOWING 1-10 OF 31 REFERENCES

Competition in periodic media: II -- Segregative limit of pulsating fronts and "Unity is not Strength"-type result

- Mathematics
- 2016

Bistable Traveling Waves for Monotone Semiflows with Applications

- Mathematics, Physics
- 2011

Propagation Phenomena for A Reaction–Advection–Diffusion Competition Model in A Periodic Habitat

- Mathematics
- 2014

Analysis of the periodically fragmented environment model: II—biological invasions and pulsating travelling fronts

- Mathematics
- 2005

Analysis of the periodically fragmented environment model : I – Species persistence

- Mathematics, Medicine
- Journal of mathematical biology
- 2005

Existence and stability of travelling wave solutions of competition models: A degree theoretic approach

- Mathematics
- 1982

Travelling waves for diffusive and strongly competitive systems: Relative motility and invasion speed

- Mathematics, Physics
- European Journal of Applied Mathematics
- 2015