In this paper we consider a modified spatiotemporal ecological system originating from the temporal Holling-Tanner model, by incorporating diffusion terms. The original ODE system is studied for the stability of coexisting homogeneous steady-states. The modified PDE system is investigated in detail with both numerical and analytical approaches. Both the Turing and non-Turing patterns are examin...

Spontaneous pattern formation in a variety of spatially extended nonlinear systems always occurs through a modulation instability, sometimes called Turing instability: the homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of sp...

We develop a four-variable model, based on the classic Field–Kőrös–Noyes mechanism for the oscillatory Belousov-Zhabotinsky BZ reaction, that describes recently discovered jumping waves and bubble waves in the BZ reaction in aerosol OT microemulsion and provides insight into their origins. Contrary to suggestions based on previous models, it appears that these phenomena can arise from interacti...

We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary ...

Promoters are adsorbed mobile species which do not directly participate in a catalytic surface reaction, but can influence its rate. Often, they are characterized by strong attractive interactions with one of the reactants. We show that these conditions lead to a Turing instability of the uniform state and to the formation of reaction-induced periodic concentration patterns. Experimentally such...

In this paper we introduce a bacteria-leukocyte model with bacteria chemotaxsis. We assume that bacteria develop a tactic defence mechanism as a response to Leukocyte phagocytosis. We explore the effect of this tactic motion on Turing space in two parameter spaces. A fine tuning of bacterial chemotaxis shows a significant effect on developing a non-uniform steady state. Keywords—Chemotaxis-diff...

In cardiac cells, the coupling between the voltage across the cell membrane (V(m)) and the release of calcium (Ca) from intracellular stores is a crucial ingredient of heart function. Under abnormal conditions and/or rapid pacing, both the action potential duration and the peak Ca concentration in the cell can exhibit well known period-doubling oscillations referred to as "alternans," which hav...

Convection-induced instability in reaction-diffusion systems produces complicated patterns of oscillations behind propagating wavefronts. We transform the system twice: into lambda-omega form, then into polar variables. We find analytical estimates for the wavefront speed which we confirm numerically. Our previous work examined a simpler system [E. H. Flach, S. Schnell, and J. Norbury, Phys. Re...

We consider the use of reaction-diffusion equations to model biological pattern formation and describe the derivation of the reaction terms for several illustrative examples. After a brief discussion of the Turing instability in such systems we extend the model formulation to incorporate domain growth. Comparisons are drawn between solution behaviour on growing domains and recent results on sel...

Abstract We propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing microzooplankton. Volatile information-conveying chemicals (infochemicals) released by play an important role in food webs of marine ecosystems. Microzooplankton is ecologically grazer coexistence large number species. Here, we discuss how information transferred dim...