Spiral Waves, Obstacles and Cardiac Arrhythmias

Olmos‐Liceaga, Daniel

doi:10.5772/31713

Cited by 1 publication

(1 citation statement)

References 42 publications

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“…Finally, in two‐dimensional reaction–diffusion systems, it is common to observe patterns that help illuminate the dynamics on the studied phenomenon. Examples of typical patterns can arise from Turing instabilities (Li, ; Sun, Jusup, Jin, Wang, & Wang, ), Turing–Hopf bifurcations (Castillo, Sánchez‐Garduño, & Padilla, ), wave splitting (Petrov, Scott, & Showalter, ), and spiral waves (Olmos‐Liceaga, ). Currently, propagation of the species with periodic invasions, given by spiral wave structures (Olmos‐Liceaga, ), is being considered, as it is a straightforward direction to go when studying excitable systems.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Diffusion as a strategy for survival in an invasion predator–prey model

Olmos‐Liceaga¹,

Villavicencio-Pulido

Acuña‐Zegarra³

2017

Natural Resource Modeling

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In some ecosystems, the invasion of species may lead to extinction or displacement of the local species that are in the medium. In this work, we present a theoretical predator–prey model based on reaction diffusion equations, where each species has a strong Allee effect. We use the diffusion coefficients as parameters in a one‐dimensional environment to show that prey can either survive or become extinct from its habitat. When the results are extended to two spatial dimensions, diffusion alone is no longer a sufficient condition in order to assure extinction or survival of the prey species; in this case, the geometry of the propagation front plays an essential role in the dynamics. Finally, a discussion about strategies for survival and extinction of the prey species is considered. The results can be useful in understanding invasion for species such as the Argentine ant Linepithema humile or to help to find control strategies for unwanted species in an ecosystem by introducing a predator.

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