In this paper we introduce a conceptual model for vegetation patterns that generalizes the Klausmeier model for semi-arid ecosystems on a sloped terrain [23]. Our model not only incorporates downhill flow, but also linear or nonlinear diffusion for the water component. To relate the model to observations and simulations in ecology, we first consider the onset of pattern formation through a Turi...

In this paper, we propose a nutrient-phytoplankton model with toxic effects governed by the Holling-type II functional. We conduct qualitative analysis on system and its steady state problem. particular, Turing instability of unique constant state, existence nonexistence nonconstant states are analyzed. Our results show some more delicate influences effect functional formation pattern, compared...

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic...

The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical Modeling (Nauka, Moscow, 1987) (in Russian), p. 5...

In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...

In this paper, the spatial, temporal and spatiotemporal dynamics of a reaction–diffusion predator–prey system with mutual interference described by the Crowley–Martin-type functional response, under homogeneous Neumann boundary conditions, are studied. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential eq...

<p style='text-indent:20px;'>A diffusive Rosenzweig-MacArthur model involving nonlocal prey competition is studied. Via considering joint effects of prey's carrying capacity and predator's diffusion rate, the first Turing (Hopf) bifurcation curve precisely described, which can help to determine parameter region where coexistence equilibrium stable. Particularly, lose its stability through...

Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equi...

We report the observation of frequency shift modulation instability sidelobes due to synchronization mismatch between pulsed pump period and resonator's round-trip time. show that a very small leads significant sidelobes. develop theory originating from absolute convective instabilities confirm experimental observations numerical simulations. The temporal drifts Turing patterns induced by are m...

Bifurcations of spatially nonhomogeneous periodic solutions and steady state solutions are rigorously proved for a reaction-diffusion system modeling CIMA chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics including Turing instability and oscillatory behavior. Examples of numerical simulation are also shown to support and strengthen t...