Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton–Zooplankton Model with Nonmonotonic Functional Response

2017 ◽  
Vol 27 (06) ◽  
pp. 1750088 ◽  
Author(s):  
Renji Han ◽  
Binxiang Dai
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Spatiotemporal Distribution ◽  
Spatiotemporal Pattern ◽  
Amplitude Equations ◽  
Toxic Phytoplankton ◽  
Cross Diffusion ◽  
The Cross ◽  
Nonmonotonic Functional Response ◽  
The Impact

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton–zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

Pattern formation by fractional cross-diffusion in a predator–prey model with Beddington–DeAngelis type functional response

2019 ◽  
Vol 33 (25) ◽  
pp. 1950296
Author(s):  
Naveed Iqbal ◽  
Ranchao Wu
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Equilibrium Points ◽  
Turing Instability ◽  
Turing Patterns ◽  
Scaling Analysis ◽  
Amplitude Equations ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
The Stability

In this paper, we explore the emergence of patterns in a fractional cross-diffusion model with Beddington–DeAngelis type functional response. First, we explore the stability of the equilibrium points with or without fractional cross-diffusion. Instability of equilibria can be induced by cross-diffusion. We perform the linear stability analysis to obtain the constraints for the Turing instability. It is found by theoretical analysis that cross-diffusion is an important mechanism for the appearance of Turing patterns. For the dynamics of pattern, the weakly nonlinear multi-scaling analysis has been performed to obtain the amplitude equations. Finally, we ensure the existence of Turing patterns such as squares, spots and stripes by using the stability analysis of the amplitude equations. Moreover, with the assistance of numerical simulations, we verify the theoretical results.

scholarly journals Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1244
Author(s):  
Maria Francesca Carfora ◽  
Isabella Torcicollo
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Fear Effect ◽  
Group Defense ◽  
The Cross ◽  
The Stability

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
J. C. Umavathi ◽  
Ali J. Chamkha
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Fluid Model ◽  
Lewis Number ◽  
Double Fourier Series ◽  
Elastic Parameter ◽  
Cross Diffusion ◽  
Nusselt Numbers ◽  
Approach To Steady State ◽  
The Impact

Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

scholarly journals Investigation of the functional network modifier loading on the stoichiometric ratio of epoxy resins and their dielectric properties

2021 ◽  
Author(s):  
Istebreq A. Saeedi ◽  
Sunny Chaudhary ◽  
Thomas Andritsch ◽  
Alun S. Vaughan
Keyword(s):  
Glass Transition ◽  
Dielectric Properties ◽  
Electrical Properties ◽  
Epoxy Resins ◽  
Functional Network ◽  
Cross Linking ◽  
Network Modifier ◽  
Epoxy Resin System ◽  
The Cross ◽  
The Impact

AbstractReactive molecular additives have often been employed to tailor the mechanical properties of epoxy resins. In addition, several studies have reported improved electrical properties in such systems, where the network architecture and included function groups have been modified through the use of so-called functional network modifier (FNM) molecules. The study reported here set out to investigate the effect of a glycidyl polyhedral oligomeric silsesquioxane (GPOSS) FNM on the cross-linking reactions, glass transition, breakdown strength and dielectric properties of an amine-cured epoxy resin system. Since many previous studies have considered POSS to act as an inorganic filler, a key aim was to consider the impact of GPOSS addition on the stoichiometry of curing. Fourier transform infrared spectroscopy revealed significant changes in the cross-linking reactions that occur if appropriate stoichiometric compensation is not made for the additional epoxide groups present on the GPOSS. These changes, in concert with the direct effect of the GPOSS itself, influence the glass transition temperature, dielectric breakdown behaviour and dielectric response of the system. Specifically, the work shows that the inclusion of GPOSS can result in beneficial changes in electrical properties, but that these gains are easily lost if consequential changes in the matrix polymer are not appropriately counteracted. Nevertheless, if the system is appropriately optimized, materials with pronounced improvements in technologically important characteristics can be designed.

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

2019 ◽  
Vol 29 (03) ◽  
pp. 1950036 ◽  
Author(s):  
R. Sivasamy ◽  
M. Sivakumar ◽  
K. Balachandran ◽  
K. Sathiyanathan
Keyword(s):  
Temporal Dynamics ◽  
Intake Rate ◽  
Diffusion Term ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting ◽  
Ratio Dependent ◽  
The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

Are neutrophil extracellular traps the link for the cross-talk between periodontitis and rheumatoid arthritis physiopathology?

Rheumatology ◽  
2021 ◽  
Author(s):  
Sicília Rezende Oliveira ◽  
José Alcides A de Arruda ◽  
Ayda Henriques Schneider ◽  
Valessa Florindo Carvalho ◽  
Caio Machado ◽  
...  
Keyword(s):  
Rheumatoid Arthritis ◽  
Cross Talk ◽  
Neutrophil Extracellular Traps ◽  
Periodontal Therapy ◽  
Clinical Parameters ◽  
Extracellular Traps ◽  
Early Ra ◽  
The Cross ◽  
High Concentrations ◽  
The Impact

Abstract Objectives Neutrophil extracellular traps (NETs) play a role in the pathogenesis of periodontitis and rheumatoid arthritis (RA). However, it remains poorly understood whether NETs participate in the cross-talk between periodontitis and RA. Herein, we investigated the production of NETs in individuals with periodontitis and RA and its association with clinical parameters. The impact of periodontal therapy on RA and NET release was also assessed. Methods The concentration of NETs and cytokines was determined in the saliva and plasma of individuals with early RA (n = 24), established RA (n = 64), and individuals without RA (n = 76). The influence of periodontitis on the production of NETs and cytokines was also evaluated. Results Individuals with early RA had a higher concentration of NETs in saliva and plasma than individuals with established RA or without RA. Periodontitis resulted in an increase in the concentration of NETs of groups of individuals without RA and with early RA. The proportion of individuals with high concentrations of IL-6, IL-10 and GM-CSF was higher among individuals with periodontitis than among individuals without periodontitis. The concentrations of TNF-α, IL-6, IL-17/IL-25, and IL-28A were particularly high in individuals with early RA. Worse periodontal clinical parameters, RA onset and RA activity were significantly associated with circulating NETs. Periodontal therapy was associated with a reduction in the concentration of NETs and inflammatory cytokines and amelioration in periodontitis and RA. Conclusion This study reveals that NETs are a possible link between periodontitis and RA, with periodontal therapy resulting in a dramatic switch in circulating NET levels.

Sign in / Sign up

Export Citation Format

Share Document