Turing instability in the reaction-diffusion network

Zheng, Qianqian; Shen, Jianwei; Xu, Yong

doi:10.1103/physreve.102.062215

Cited by 35 publications

(14 citation statements)

References 36 publications

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“…Hopf and Turing bifurcations are obtained. When condition (11) holds, the network system always undergoes Hopf bifurcation and Turing bifurcation regardless of the network connection probability p [ Figures 3,4,5,6,and 11]. Namely, regardless of how the network nodes are connected, prey and predators will coexist, and the system will oscillate periodically.…”

Section: Discussionmentioning

confidence: 99%

“…Colorful patterns emerge from reaction-diffusion equations and can explain a wide variety of natural phenomena. Since Turing published his groundbreaking work [1], the Turing pattern has received increasing attention in biology, physics, chemicals, and other fields [2,3,4,5]. At present, it has been applied to more complex interdisciplinary subjects.…”

Section: Introductionmentioning

confidence: 99%

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Delay-induced self-organization dynamics in a prey-predator network with diffusion

Shen

2022

Nonlinear Dyn

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Time delays can induce the loss of stability and degradation of performance. In this paper, the pattern dynamics of a prey-predator network with diffusion and delay are investigated, where the inhomogeneous distribution of species in space can be viewed as a random network, and delay can affect the stability of the network system. Our results show that time delay can induce the emergence of Hopf and Turing bifurcations, which are independent of the network, and the conditions of bifurcation are derived by linear stability analysis. Moreover, we find that the Turing pattern can be related to the network connection probability. The Turing instability region involving delay and network connection probability is obtained. Finally, the numerical simulation verifies our results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delay-induced self-organization dynamics in a prey-predator network with diffusion

Shen

2022

Nonlinear Dyn

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“…

(

) if and only if a

makes

(

) hold. Therefore, the stability of system (2) is determined by the stability of system (1) in a sense [20] , [37] .…”

Section: The Network-organized Sir Modelmentioning

confidence: 99%

“…Although Zheng et al. reported promising results about negative wavenumber [20] , the role of negative wavenumber in the Turing instability is still unresolved, especially for saddle–node in the network-organized SIR model.…”

Section: Introductionmentioning

confidence: 99%

Pattern mechanism in stochastic SIR networks with ER connectivity

Zheng

Shen

et al. 2022

Physica A: Statistical Mechanics and its Applications

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“…Therefore, when summarizing the applications of MG‐based materials in electrocatalysis and energy storage, we focus on the relationships between the kinetic parameters commonly used in different reaction systems and the unique composition and structure of materials. So far, tens of thousands of MGs, such as Zr‐, [ 23 ] Fe‐, [ 24 ] Ni‐, [ 25 ] Cu‐, [ 9 ] Pd‐, [ 7 ] Mg‐, [ 26 ] Au‐, [ 27 ] Pt‐based ones [ 28 ] with superb stability and electrical activity have been developed to satisfy different requirements. Nevertheless, compared with traditional crystalline materials, the utilization of MG‐based materials is limited in energy field.…”

Section: Introductionmentioning

confidence: 99%

Progress and Perspective of Metallic Glasses for Energy Conversion and Storage

Jiang

Chen

et al. 2022

Advanced Energy Materials

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Owing to its unique atomic arrangement and electronic structure, metallic glass (MG) has been widely investigated in the field of energy storage and conversion. In the past few decades, multiple strategies have been developed to synthesize bulk and nanosized MG based materials. Here, combining the structure–activity relationship of MG with electrochemical reaction kinetics, the substantial progress of glass structures in electrocatalytic processes are highlighted, including the hydrogen evolution reaction, oxygen evolution reaction, oxygen reduction reaction, methanol oxidation reaction, carbon dioxide reduction reaction, and nitrogen fixation. Meanwhile, applications of MG materials in energy storage devices, like supercapacitors and lithium‐ion batteries, are also introduced in detail. Finally, challenges and possibilities for reasonable design of highly‐efficient MG‐based electrode materials are proposed. The integration of high‐throughput methods, artificial intelligence technology, as well as advanced characterization techniques is fundamental to screen materials with remarkable performance. This review aims to deepen the understanding of the relationship between electronic structure and electrochemical performance, providing guidance for rational design of functional MG materials with outstanding activity, selectivity, and durability.

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Turing instability in the reaction-diffusion network

Cited by 35 publications

References 36 publications

Delay-induced self-organization dynamics in a prey-predator network with diffusion

Delay-induced self-organization dynamics in a prey-predator network with diffusion

Pattern mechanism in stochastic SIR networks with ER connectivity

Progress and Perspective of Metallic Glasses for Energy Conversion and Storage

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