diffusive system
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2021 ◽  
Author(s):  
Yehu Lv

Abstract In this paper, by incorporating the general delay to the reaction term in the memory-based diffusive system, we propose a diffusive system with memory delay and general delay (e.g., gestation, hunting, migration and maturation delays, etc.). We first derive an algorithm for calculating the normal form of Hopf bifurcation in a diffusive system with memory and general delays. The developed algorithm for calculating the normal form can be used to investigate the direction and stability of Hopf bifurcation. Then, we consider a diffusive predator-prey model with ratio-dependent Holling type-3 functional response, which includes with memory and gestation delays. The Hopf bifurcation analysis without considering gestation delay is first studied, then the Hopf bifurcation analysis with memory and gestation delays is studied. Furthermore, by using the developed algorithm for calculating the normal form, the supercritical and stable spatially homogeneous periodic solutions induced jointly by memory and general delays are found theoretically. The stable spatially homogeneous periodic solutions are also found by the numerical simulations which confirms our analytic result.


2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Pei-Chao Cao ◽  
Ying Li ◽  
Yu-Gui Peng ◽  
Minghong Qi ◽  
Wen-Xi Huang ◽  
...  

AbstractNon-Hermitian wave system has attracted intense attentions in the past decade since it reveals interesting physics and generates various counterintuitive effects. However, in the diffusive system that is inherently non-Hermitian with natural dissipation, the robust control of heat flow is hitherto still a challenge. Here we introduce the skin effect into diffusive systems. Different from the skin effect in wave systems, where asymmetric couplings were enabled by dynamic modulations or judicious gain/loss engineering, asymmetric couplings of the temperature fields in diffusive systems can be realized by directly contacted metamaterial channels. Topological heat funneling is further presented, where the temperature field automatically concentrates towards a designated position and shows a strong immunity against the defects. Our work indicates that the diffusive system can provide a distinctive platform for exploring non-Hermitian physics as well as thermal topology.


2020 ◽  
Author(s):  
Gaspard Farge ◽  
Nikolai Shapiro ◽  
Claude Jaupart ◽  
Édouard Kaminski

<p>The activity of slow-earthquakes in subduction zones have been closely linked to fluid circulation processes — like hydro fracturation and pore-pressure pulses — on the one hand by geological observations and on the other hand by slow-earthquake triggering and interaction models. In deep fault zone environments, where slow slip events and various regimes of tremor are observed, fluids coming from metamorphic dehydration of slab sediments are channeled towards the surface. Geological observations indicate that fluid transport conditions vary significantly on short time scales, and along dip, strike and width of the fault zone. In homogeneously permeable systems where fluids transit under stable conditions, pore-pressure can be described by a diffusion equation. We use a time and space bimodal description of the transport properties to model a tremor generating, permeable fault zone. Thin zones of low permeability acting as valves are distributed along the 1D channel with a higher background permeability. When a threshold pore-pressure differential is reached, the valve permeability is brought to background levels, until the barrier is healed and closes again. In this model, the opening of a valve occurs at the same time as the source of a low-frequency earthquake (LFE) is triggered. In such a set up, sources interact uniquely due to the channeling of stress through pore-pressure diffusion, and the interaction characteristics in time/space are described in the framework of a diffusive system. When the number of sources is high, the model can reproduce clustering behaviours observed for LFE activity in subduction zones. The transition from a Poisson process description of seismicity to highly clustered, cascading events is governed by the source interaction distances, directly relating to the transport properties of the medium. In time, such a model is meant to diagnose the transport conditions in a subduction zone or a magmatic system, provided that it can be characterized by clustering statistics on the low-frequency seismicity it generates.</p>


2020 ◽  
Vol 15 ◽  
pp. 23 ◽  
Author(s):  
Fethi Souna ◽  
Salih Djilali ◽  
Fayssal Charif

In this paper, we consider a new approach of prey escaping from herd in a predator-prey model with the presence of spatial diffusion. First, the sensitivity of the equilibrium state density with respect to the escaping rate has been studied. Then, the analysis of the non diffusive system was investigated where boundedness, local, global stability, Hopf bifurcation are obtained. Besides, for the diffusive system, we proved the occurrence of Hopf bifurcation and the non existence of diffusion driven instability. Furthermore, the direction of Hopf bifurcation has been proved using the normal form on the center manifold. Some numerical simulations have been used to illustrate the obtained results.


2019 ◽  
Vol 29 (14) ◽  
pp. 1930040 ◽  
Author(s):  
Qianqian Zheng ◽  
Jianwei Shen ◽  
Zhijie Wang

P53 plays a vital role in DNA repair, and several mathematical models of the p53-Mdm2 feedback loop were used to explain the biological mechanism. In this paper, a p53-Mdm2 model described by a delay reaction–diffusion equation is studied both analytically and numerically. This research aims to provide an understanding of the impact of delay and sustained pressure on the p53-Mdm2 dynamics and tries to explain some biological mechanism. It is found that the type of pattern formation is affected by Hopf bifurcation. Also, the amplitude equation in delay diffusive system is derived and it is shown that sustained stress plays an essential role in the function of p53. Finally, simulation is used to verify the theoretical results.


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