SPATIAL PATTERN IN AN EPIDEMIC SYSTEM WITH CROSS-DIFFUSION OF THE SUSCEPTIBLE

2009 ◽  
Vol 17 (01) ◽  
pp. 141-152 ◽  
Author(s):  
GUI-QUAN SUN ◽  
ZHEN JIN ◽  
QUAN-XING LIU ◽  
LI LI
Keyword(s):  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Parameter Space ◽  
Spatial Model ◽  
Great Influence ◽  
Phase Dynamics ◽  
Cross Diffusion

In this paper, pattern formation of a spatial model with cross diffusion of the susceptible is investigated. We compute Hopf and Turing bifurcations for the model. In particular, the exact Turing domain is delineated in the parameter space. When the parameters are in that domain, a series of numerical simulations reveals that the typical dynamics of the infecteds class typically involves the formation of isolated groups, i.e., striped, spotted or labyrinthine patterns. Furthermore, spatial oscillatory and anti-phase dynamics of different spatial points were also found. These results demonstrate that cross diffusion of susceptibles may have great influence on the spread of the epidemic.

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

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
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.

CROSS-DIFFUSION-DRIVEN PATTERN FORMATION AND SELECTION IN A MODIFIED LESLIE–GOWER PREDATOR–PREY MODEL WITH FEAR EFFECT

2020 ◽  
Vol 28 (01) ◽  
pp. 27-64 ◽  
Author(s):  
RENJI HAN ◽  
LAKSHMI NARAYAN GUIN ◽  
BINXIANG DAI
Keyword(s):  
Pattern Formation ◽  
Diffusion Processes ◽  
Great Influence ◽  
Spatiotemporal Pattern ◽  
Type Model ◽  
Inhomogeneous Distribution ◽  
Stripe Pattern ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Spatially Inhomogeneous

Spatial patterns through diffusion-driven instability are stationary structures that appear spontaneously upon breaking the symmetry of the spatial domain, which results only from the coupling between the reaction and the diffusion processes. This paper is concerned with a modified Leslie–Gower-type model with cross-diffusion and indirect predation effect. We first prove the global existence, non-negativity and uniform boundedness for the considered model. Then the linear stability analysis shows that the cross-diffusion is the key mechanism of spatiotemporal pattern formation. Amplitude equations are derived near Turing bifurcation point under nonlinear cross-diffusion to interpret pattern selection among spot pattern, stripe pattern and the mixture of spot and stripe patterns, which reflects the species’s spatially inhomogeneous distribution, and it is also found that the fear factor has great influence on spatially inhomogeneous distribution of the two species under certain cross-diffusivity, that is, high level of fear can induce striped inhomogeneous distribution, low level of fear can induce spotted inhomogeneous distribution, and the intermediate level of fear can induce the mixture of spotted and striped inhomogeneous distribution. Finally, numerical simulations illustrate the effectiveness of all theoretical results.

scholarly journals Quantifying ionospheric effects on global 21-cm observations

2021 ◽  
Vol 503 (1) ◽  
pp. 344-353
Author(s):  
Emma Shen ◽  
Dominic Anstey ◽  
Eloy de Lera Acedo ◽  
Anastasia Fialkov ◽  
Will Handley
Keyword(s):  
Parameter Space ◽  
Spatial Model ◽  
Ionospheric Effects ◽  
Temporal Variance ◽  
Foreground Calibration ◽  
Over Time

ABSTRACT We modelled the two major layer of Earth’s ionosphere, the F-layer and the D-layer, by a simplified spatial model with temporal variance to study the chromatic ionospheric effects on global 21-cm observations. From the analyses, we found that the magnitude of the ionospheric disruptions due to ionospheric refraction and absorption can be greater than the expected global 21-cm signal, and the variation of its magnitude can differ, depending on the ionospheric conditions. Within the parameter space adopted in the model, the shape of the global 21-cm signal is distorted after propagating through the ionosphere, while its amplitude is weakened. It is observed that the ionospheric effects do not cancel out over time, and thus should be accounted for in the foreground calibration at each timestep to account for the chromaticity introduced by the ionosphere.

Spatial-Pattern-Induced Evolution of a Self-Replicating Loop Network

2006 ◽  
Vol 12 (4) ◽  
pp. 461-485 ◽  
Author(s):  
Keisuke Suzuki ◽  
Takashi Ikegami
Keyword(s):  
Pattern Formation ◽  
Spatial Pattern ◽  
Spatial Patterns ◽  
Spiral Structure ◽  
Scale Interactions ◽  
Micro Scale ◽  
Macro Scale ◽  
Loop Network ◽  
Spatial Pattern Formation

We study a system of self-replicating loops in which interaction rules between individuals allow competition that leads to the formation of a hypercycle-like network. The main feature of the model is the multiple layers of interaction between loops, which lead to both global spatial patterns and local replication. The network of loops manifests itself as a spiral structure from which new kinds of self-replicating loops emerge at the boundaries between different species. In these regions, larger and more complex self-replicating loops live for longer periods of time, managing to self-replicate in spite of their slower replication. Of particular interest is how micro-scale interactions between replicators lead to macro-scale spatial pattern formation, and how these macro-scale patterns in turn perturb the micro-scale replication dynamics.

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