<title>Numerical simulations of nonparaxial beam self-action and transverse pattern formation in nonlinear media</title>

We propose a novel semiconductor device in which electronic-analogue dendritic trees grow on multilayer single-electron circuits. A simple cellular-automaton circuit was designed for generating dendritic patterns by utilizing the physical properties of single-electron devices, i.e. quantum and thermal effects in tunneling junctions. We demonstrate typical operations of the proposed circuit through extensive numerical simulations.

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Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

International Journal of Biomathematics ◽

10.1142/s1793524517500735 ◽

2017 ◽

Vol 10 (05) ◽

pp. 1750073 ◽

Cited By ~ 1

Author(s):

Peng Feng

Keyword(s):

Steady State ◽

Pattern Formation ◽

Spatial Pattern ◽

Numerical Simulations ◽

Functional Response ◽

Allee Effect ◽

Turing Instability ◽

Spatial Pattern Formation ◽

The Stability ◽

Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

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Numerical simulations of the effects of retinoids on pattern formation in a hydroid

Wilhelm Roux s Archives of Developmental Biology ◽

10.1007/bf00456109 ◽

1986 ◽

Vol 195 (2) ◽

pp. 128-132 ◽

Cited By ~ 1

Author(s):

Wolf Kemmner

Keyword(s):

Pattern Formation ◽

Numerical Simulations

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Numerical Simulations of Elliptical Hollow Gaussian Beams Propagating in Strongly Nonlocal Media

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.713-715.2085 ◽

2015 ◽

Vol 713-715 ◽

pp. 2085-2088

Author(s):

Zhen Feng Yang

Keyword(s):

Numerical Simulations ◽

Beam Width ◽

Input Power ◽

Gaussian Beams ◽

Nonlinear Media ◽

Nonlocal Nonlinear Media ◽

Strongly Nonlocal Nonlinear Media ◽

Nonlocal Media ◽

Nonlocal Nonlinear ◽

Evolution Period

The evolution of elliptical hollow Gaussian beams propagating in strongly nonlocal nonlinear media is investigated. As examples, this paper mainly focuses on the evolutions of the transverse intensity and the beam width of elliptical hollow Gaussian beams with the beam order being 1 and 3. The results show that the evolutions of the transverse intensity and the beam width are both periodical and the size of the evolution period is determined by the input power. There exists the transverse reverse transform for the beam width when selecting a proper input power, which is quiet different from the circularly symmetric hollow Gaussian beams.

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Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion

European Journal of Applied Mathematics ◽

10.1017/s0956792520000248 ◽

2020 ◽

pp. 1-31

Author(s):

HAI-YANG JIN ◽

ZHI-AN WANG

Keyword(s):

Pattern Formation ◽

Numerical Simulations ◽

Prey Density ◽

Temporal Patterns ◽

Steady States ◽

Global Dynamics ◽

Predator Prey ◽

Density Dependent ◽

Spatially Homogeneous ◽

Spatio Temporal

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator–prey systems with density-dependent prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusiq‘dfdon) and mobility (prey-taxis) of the predator are correlated through a prey density-dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals. With numerical simulations, we further demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possible for the parameters outside the stability regime. We also find from numerical simulations that the temporal dynamics between linearised system and nonlinear systems are quite different, and the prey density-dependent motility function can trigger the pattern formation.

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