Related papers: Short-wave signal versus indirect prey-taxis
We consider a model of the predator--prey community with prey-taxis. By that we mean the capability of the predators to get moving in a certain direction on the macroscopic level in response to the prey density gradients. Additionally, we…
We consider two models of predator-prey community with prey-taxis, one relies on Patlak-Keller-Segel law (Lee et al, 2009), the other one employs the Cattaneo model of heat transfer following Dolak and Hillen (2003). Thus, the former one…
This article aims at exploring the short-wavelength stabilization and destabilization of the advection-diffusion systems formulated using the Patlak-Keller-Segel cross-diffusion. We study a model of the taxis partly driven by an external…
In this article we study the stabilizing of a primitive pattern of behaviour for the two-species community with chemotaxis due to the short-wavelength external signal. We use a system of Patlak-Keller-Segel type as a model of the community.…
We have studied properties of nonlinear 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. The mechanism of propagation of these waves essentially…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We propose and study a class of parabolic-ODE models involving chemotaxis and haptotaxis of a species following signals indirectly produced by another, non-motile one. The setting is motivated by cancer invasion mediated by interactions…
We study the weak interaction between a pair of well-separated coherent structures in possibly non-local lattice differential equations. In particular we prove that if a lattice differential equation in one space dimension has…
This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…
This paper concerns with the global dynamics of classical solutions to an important alarm-taxis ecosystem, which demonstrates the behaviors of prey that attract secondary predator when threatened by primary predator. And the secondary…
In the framework of chaotic scattering we analyze passive tracer transport in finite systems. In particular, we study models with open streamlines and a finite number of recirculation zones. In the non trivial case with a small number of…
In this manuscript, an attempt has been made to understand the effects of prey-taxis on the existence of global-in-time solutions and dynamics in an eco-epidemiological model, particularly under the influence of slow dispersal characterized…
We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive…
The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
We provide a detailed study of the dynamics obtained by linearizing the Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal wave. In a suitable sense, linearly analogous to space-modulated stability, we prove…
This article considers a class of Lotka-Volterra systems with multiple nonlinear cross-diffusion, commonly known as prey-taxis models. The existence and stability of classic solutions for such systems with spatially homogeneous sources and…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…
We study the regularity and large-time behavior of a crowd of species driven by chemo-tactic interactions. What distinguishes the different species is the way they interact with the rest of the crowd: the collective motion is driven by…