# A Minimal Model of Pursuit-Evasion in a Predator-Prey System

Y. Tyutyunov; L. Titova; R. Arditi

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 4, page 122-134
- ISSN: 0973-5348

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topTyutyunov, Y., Titova, L., and Arditi, R.. "A Minimal Model of Pursuit-Evasion in a Predator-Prey System." Mathematical Modelling of Natural Phenomena 2.4 (2010): 122-134. <http://eudml.org/doc/222438>.

@article{Tyutyunov2010,

abstract = {
A conceptual minimal model demonstrating spatially heterogeneous wave regimes
interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The
model is based on the earlier proposed hypothesis that taxis accelerations of prey and
predators are proportional to the density gradient of another population playing a role
of taxis stimulus. Considering acceleration rather than immediate velocity allows
obtaining realistic solutions even while ignoring variations of total abundances of both
modelled populations. Linear analysis of the model shows that stationary homogeneous
regime becomes oscillatory unstable with respect to small heterogeneous perturbations
if either taxis activities or total population abundances are high enough. The ability
for active directed movement of both prey and predators is the necessary condition for
spatial self-organization. Numerical simulations illustrate analytical results.
The relation between the proposed model and conventional two-component systems with
cross-diffusion is discussed.
},

author = {Tyutyunov, Y., Titova, L., Arditi, R.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {taxis-diffusion-reaction; attraction-repulsion; prey-taxis; tropho-taxis;
population clustering; population wave; spatial heterogeneity; spatial behaviour; population clustering},

language = {eng},

month = {3},

number = {4},

pages = {122-134},

publisher = {EDP Sciences},

title = {A Minimal Model of Pursuit-Evasion in a Predator-Prey System},

url = {http://eudml.org/doc/222438},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Tyutyunov, Y.

AU - Titova, L.

AU - Arditi, R.

TI - A Minimal Model of Pursuit-Evasion in a Predator-Prey System

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 2

IS - 4

SP - 122

EP - 134

AB -
A conceptual minimal model demonstrating spatially heterogeneous wave regimes
interpreted as pursuit-evasion in predator-prey system is constructed and investigated. The
model is based on the earlier proposed hypothesis that taxis accelerations of prey and
predators are proportional to the density gradient of another population playing a role
of taxis stimulus. Considering acceleration rather than immediate velocity allows
obtaining realistic solutions even while ignoring variations of total abundances of both
modelled populations. Linear analysis of the model shows that stationary homogeneous
regime becomes oscillatory unstable with respect to small heterogeneous perturbations
if either taxis activities or total population abundances are high enough. The ability
for active directed movement of both prey and predators is the necessary condition for
spatial self-organization. Numerical simulations illustrate analytical results.
The relation between the proposed model and conventional two-component systems with
cross-diffusion is discussed.

LA - eng

KW - taxis-diffusion-reaction; attraction-repulsion; prey-taxis; tropho-taxis;
population clustering; population wave; spatial heterogeneity; spatial behaviour; population clustering

UR - http://eudml.org/doc/222438

ER -

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