A predator–prey interaction model with self and cross-diffusion

B Dubey, B Das, J Hussain - Ecological Modelling, 2001 - Elsevier
In this paper, a mathematical model for a predator–prey interaction with self and cross-
diffusion is proposed and analysed. Criteria for local stability, instability and global stability …

A non-local cross-diffusion model of population dynamics I: emergent spatial and spatiotemporal patterns

NP Taylor, H Kim, AL Krause… - Bulletin of Mathematical …, 2020 - Springer
We extend a spatially non-local cross-diffusion model of aggregation between multiple
species with directed motion toward resource gradients to include many species and more …

On the degradation of forest ecosystems by extreme events: Statistical Model Checking of a hybrid model

G Cantin, B Delahaye, BM Funatsu - Ecological Complexity, 2023 - Elsevier
In this paper, we study the vulnerability of forest ecosystems perturbed by extreme events,
such as those arising from climate change. To investigate the complex interactions between …

On the robustness of discontinuous patterns in degenerate reaction–diffusion systems with perturbed hysteresis

G Cantin - Communications in Nonlinear Science and Numerical …, 2024 - Elsevier
In this paper, we study the dynamics of a morphogenesis model which reproduces the
formation of discontinuous patterns observed in numerous biological or ecological systems …

Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator–prey pursuit and evasion example

MA Tsyganov, J Brindley, AV Holden… - Physica D: Nonlinear …, 2004 - Elsevier
We have studied properties of non-linear waves in a mathematical model of a predator–prey
system with pursuit and evasion. We demonstrate a new type of propagating wave in this …

Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion

EP Zemskov, MA Tsyganov, W Horsthemke - Physical Review E, 2017 - APS
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system
with linear cross diffusion. To be specific, we consider a piecewise linear approximation of …

Networks of forest ecosystems: Mathematical modeling of their biotic pump mechanism and resilience to certain patch deforestation

G Cantin, N Verdière - Ecological Complexity, 2020 - Elsevier
We propose an innovative mathematical model for studying the dynamics of a complex
network of forest ecosystems, in which two forest patches interact which each other through …

Non-existence of the global attractor for a partly dissipative reaction-diffusion system with hysteresis

G Cantin - Journal of Differential Equations, 2021 - Elsevier
The asymptotic behavior of a partly dissipative reaction-diffusion system with hysteresis is
investigated. This system describes the dynamics of forest ecosystems and reproduces the …

A non-local cross-diffusion model of population dynamics II: Exact, approximate, and numerical traveling waves in single-and multi-species populations

AL Krause, RA Van Gorder - Bulletin of Mathematical Biology, 2020 - Springer
We study traveling waves in a non-local cross-diffusion-type model, where organisms move
along gradients in population densities. Such models are valuable for understanding waves …

Solitary waves in excitable systems with cross-diffusion

VN Biktashev, MA Tsyganov - Proceedings of the …, 2005 - royalsocietypublishing.org
We consider a FitzHugh–Nagumo system of equations where the traditional diffusion terms
are replaced with linear cross-diffusion of components. This system describes solitary waves …