In this manuscript, we consider temporal and spatio-temporal modified Holling–Tanner predator-prey models with growth rate as a logistic type, Holling type II functional response alternative food sources for the predator. From our result of model, identify regions in parameter space which Turing instability model is expected show numerical evidence where leads to periodic solutions. Subsequentl...

This talk will focus on the underlying questions in development and to a lesser degree, chemistry, perhaps discuss in general terms Turing theory, positional information, gradient theories, mechanochemical theories, and availability of data, etc. 10:30 am Coffee Break Lind Hall Room 400 11:00 am Hans Othmer University of Utah An Introduction to Turing Theory Abstract: The basic mathematical the...

Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system the presence of spatial heterogeneity both transport reaction terms. Under suitable asymptotic assumption that is slow over domain, while gradients are not too sharp, stability steady state approximated absence transport. U...

In this paper, we study the dynamic phase transition for one dimensional Brusselator model. By linear stability analysis, define two critical numbers \begin{document}$ {\lambda}_0 $\end{document} and id="M2">\begin{document}$ {\lambda}_1 control parameter id="M3">\begin{document}$ {\lambda} in equation. M...

In this paper, first we consider the global dynamics of a ratio-dependent predator–prey model with density dependent death rate for the predator species. Analytical conditions for local bifurcation and numerical investigations to identify the global bifurcations help us to prepare a complete bifurcation diagram for the concerned model. All possible phase portraits related to the stability and i...

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises a variety settings, including applications developmental biology, spatial ecology, and experimental chemistry. Analyzing such is complicated, as there strong dependence any spatially homogeneous base states time, the resulting structure linearized perturbations used to ...

BACKGROUND Physical scaffolds are useful for supporting cells to form three-dimensional (3D) tissue. However, it is non-trivial to develop a scheme that can robustly guide cells to self-organize into a tissue with the desired 3D spatial structures. To achieve this goal, the rational regulation of cellular self-organization in 3D extracellular matrix (ECM) such as hydrogel is needed. RESULTS I...