Related papers: Classical and generalized solutions of an alarm-ta…

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…

This paper is concerned with the global boundedness and stability of classical solutions to an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism of anti-predation behavior when species are threaten by…

This paper is concerned with positive solutions of boundary value problems \begin{equation*} \left\{\begin{array}{ll} {\rm div}\left(d(v)\nabla u-u\chi(v)\nabla v\right)+\lambda u-u^2 +\gamma u F(v)=0, & x \in \Omega,\\[1mm] D \Delta v+\mu…

This study examines a fully parabolic predator-prey chemo-alarm-taxis system under homogeneous Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ with a smooth boundary $\partial\Omega$. Under specific parameter…

We study the system \begin{align*}\label{prob:star} \tag{$\star$} \begin{cases} u_t = D_1 \Delta u - \chi_1 \nabla \cdot (u \nabla v) + u(\lambda_1 - \mu_1 u + a_1 v) \\ v_t = D_2 \Delta v + \chi_2 \nabla \cdot (v \nabla u) + v(\lambda_2 -…

This paper is concerned with a diffusive predator-prey model with predator-taxis and prey-taxis. Based on the Schauder fixed point theorem, we prove the global existence, uniqueness and boundedness of the classical solutions under the…

Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…

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…

We consider the system \[ \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot ( \tfrac{u}{v} \nabla v) - uv + \rho u - \mu u^2, \\ v_t &= \Delta v - v + u v \end{aligned} \right. \tag{$\star$} \] with $\rho \in \mathbb{R}, \mu > 0,…

This manuscript considers a Neumann initial-boundary value problem for the predator-prey system $$ \left\{ \begin{array}{l} u_t = D_1 u_{xx} - \chi_1 (uv_x)_x + u(\lambda_1-u+a_1 v), \\[1mm] v_t = D_2 v_{xx} + \chi_2 (vu_x)_x +…

Many ecological population models consider taxis as the directed movement of animals in response to a stimulus. The taxis is named direct if the animals are guided by the density gradient of some other population or indirect if they are…

The role of predator evasion mediated by chemical signaling is studied in a diffusive prey-predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients $\chi$ and $\xi$ respectively. In…

The diffusive Lotka-Volterra predator-prey model \begin{eqnarray*} \left\{ \begin{array}{rcll} u_t &=& \nabla\cdot \left[ d_1\nabla u + \chi v^2 \nabla \Big(\dfrac{u}{v}\Big)\right] +u(m_1-u+av), \qquad & x\in\Omega, \ t>0, \\ v_t &=&…

We consider the following chemotaxis systems $$\begin{cases}u_t=\Delta u-\chi_1\nabla(u\nabla v_1)+\chi_2\nabla(u\nabla v_2)+u(a-bu),\ \ x\in\mathbb R^N,t>0,\\0=(\Delta-\lambda_1I)v_1+\mu_1u,\ \ x\in\mathbb…

This work addresses the one-dimensional Cauchy problem for the doubly degenerate nutrient taxis model \begin{equation*} \begin{cases} \displaystyle \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}(u v u_x) -…

We study a doubly tactic resource consumption model \bess \left\{\begin{array}{lll} u_t=\tr u-\nabla\cd(u\nabla w),\\[1mm] v_t=\tr v-\nabla\cd(v\nabla u)+v(1-v^{\beta-1}),\\[1mm] w_t=\tr w-(u+v)w-w+r \end{array}\right. \eess in a smooth…

Assuming that $0<\chi<\sqrt{\frac{2}n}$, $\kappa\ge 0$ and $\mu>\frac{n-2}{n}$, we prove global existence of classical solutions to a chemotaxis system slightly generalizing \[ \begin{split} u_t &= \Delta u - \chi \nabla\cdot ( \frac{u}{v}…

This paper is concerned with the doubly degenerate nutrient taxis system $u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ uv$ and $v_t=\Delta v-u v$ for some $l \geqslant 1$, subjected to homogeneous Neumann…

In this article we consider a cascaded taxis model for two proliferating and degrading species which thrive on the same nutrient but orient their movement according to different schemes. In particular, we assume the first group, the…

In this paper, we are concerned with the following prey-taxis system with fluid surrounding describing by the incompressible Navier-Stokes equations in a bounded domain with smooth boundary. We show that it has global classical solutions…