A predator–prey interaction model with self and cross-diffusion
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 …
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
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 …
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
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 …
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 …
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 …
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
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 …
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 …
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 …
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
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 …
along gradients in population densities. Such models are valuable for understanding waves …
Solitary waves in excitable systems with cross-diffusion
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 …
are replaced with linear cross-diffusion of components. This system describes solitary waves …