Complex Fractional-order HIV Diffusion Model Based on Amplitude Equations with Turing Patterns and Turing Instability

Anisotropic Diffusion Model Based on a New Diffusion Coefficient and Fractional Order Differential for Image Denoising

International Journal of Image and Graphics ◽

10.1142/s0219467816500030 ◽

2016 ◽

Vol 16 (01) ◽

pp. 1650003 ◽

Cited By ~ 2

Author(s):

Jianjun Yuan ◽

Lipei Liu

Keyword(s):

Diffusion Coefficient ◽

Image Denoising ◽

Diffusion Model ◽

Fractional Order ◽

Anisotropic Diffusion ◽

Model Based ◽

Proposed Model

This paper presents an improved anisotropic diffusion model which is based on a new diffusion coefficient and fractional order differential for image denoising. In the proposed model, the new diffusion coefficient can protect edges and fine characteristics from being over-smoothed. The fractional order differential is applied to weaken the staircasing effect, preserve fine characteristics. Additionally, the automatic set method of diffusion coefficient threshold is developed. Comparative experiments show that the proposed model succeeds in denoising and preserving fine characteristics.

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Turing Patterns for a Nonlocal Lotka–Volterra Cooperative System

Journal of Nonlinear Mathematical Physics ◽

10.1007/s44198-021-00002-z ◽

2021 ◽

Vol 28 (4) ◽

pp. 363-389

Author(s):

Shao-Yue Mi ◽

Bang-Sheng Han ◽

Yu-Tong Zhao

Keyword(s):

Multiple Scale ◽

Turing Instability ◽

Turing Patterns ◽

Scale Analysis ◽

Cooperative System ◽

Amplitude Equations ◽

Pattern Dynamics ◽

Pattern Structures ◽

New Phenomena ◽

Multiple Scale Analysis

AbstractThis paper is devoted to investigating the pattern dynamics of Lotka–Volterra cooperative system with nonlocal effect and finding some new phenomena. Firstly, by discussing the Turing bifurcation, we build the conditions of Turing instability, which indicates the emergence of Turing patterns in this system. Then, by using multiple scale analysis, we obtain the amplitude equations about different Turing patterns. Furthermore, all possible pattern structures of the model are obtained through some transformation and stability analysis. Finally, two new patterns of the system are given by numerical simulation.

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

International Journal of Modern Physics B ◽

10.1142/s0217979219502965 ◽

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.

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