Related papers: Spatiotemporal dynamics in a spatial plankton syst…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
Discontinuous Shear Thickening (DST) fluids exhibit unique instability properties in a wide range of flow conditions. We present numerical simulations of a scalar model for DST fluids in a planar simple shear using the Smoothed Particle…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We investigate epidemic models with spatial structure based on the cellular automata method. The construction of the cellular automata is from the study by Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749…
Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatio-temporal forcing in the form of a travelling wave modulation of a control parameter. We show that from strictly spatial resonance, it is…
We investigate the dynamics of a discrete phytoplankton-zooplankton model incorporating Holling type~III predation and Holling type~II toxin release. The existence and stability of positive fixed points are analyzed, and it is shown that…
We study the dynamics of a discrete phytoplankton-zooplankton model with Holling type~II grazing and Holling type~III toxin release. The existence and stability of positive fixed points are analyzed, and conditions for the occurrence of…
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic…
We investigate the dynamics of multi-lump waves in a new version of a generalized spatial-symmetric higher-dimensional nonlinear dispersive water wave model using an analytical approach. This involves the proposition of a new…
We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability…