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multiple equilibria in a Land–Atmosphere Coupled System

Journal of Meteorological Research 2018年第6期32卷 950-973页

作者： Dongdong LI Yongli HE Jianping HUANG Lu BI Lei DING Key Laboratory for Semi-Arid Climate Change of the Ministry of Education College of Atmospheric Sciences Lanzhou University

Many low-order modeling studies indicate that there may be multiple equilibria in the atmosphere induced by thermal and topographic forcings.However,most work uses uncoupled atmospheric model and just focuses on the multiple equilibria with distinct wave amplitude,i.e.,the high-and low-index equilibria.Here,a low-order coupled land–atmosphere model is used to study the multiple equilibria with both distinct wave phase and wave amplitude.The model combines a two-layer quasi-geostrophic channel model and an energy balance model.Highly truncated spectral expansions are used and the results show that there may be two stable equilibria with distinct wave phase relative to the topography:one(the other)has a lower layer streamfunction that is nearly in(out of)phase with the topography,i.e.,the lower layer ridges(troughs)are over the mountains,called ridge-type(trough-type)equilibria.The wave phase of equilibrium state depends on the direction of lower layer zonal wind and horizontal scale of the topography.The multiple wave phase equilibria associated with ridge-and trough-types originate from the orographic instability of the Hadley circulation,which is a pitch-fork bifurcation.Compared with the uncoupled model,the land–atmosphere coupled system produces more stable atmospheric flow and more ridge-type equilibrium states,particularly,these effects are primarily attributed to the longwave radiation fluxes.The upper layer streamfunctions of both ridge-and trough-type equilibria are also characterized by either a high-or low-index flow pattern.However,the multiple wave phase equilibria associated with ridge-and trough-types are more prominent than multiple wave amplitude equilibria associated with high-and low-index types in this study.

关键词： multiple equilibria land–atmosphere coupling wave phase longwave radiation stability

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μ-stability of multiple equilibria in Cohen-Grossberg neural networks and its application to associative memory

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中国科学:技术科学英文版 2023年第9期66卷 2611-2624页

作者： LIU Yang WANG Zhen XIAO Min LI YuXia SHEN Hao College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China College of Automation&College of Artificial Intelligence Nanjing University of Posts and TelecommunicationsNanjing 210023China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China Electrical and Information Engineering Anhui University of TechnologyMa’anshan 243002China

In this paper, the μ-stability of multiple equilibrium points(EPs) in the Cohen-Grossberg neural networks(CGNNs) is addressed by designing a kind of discontinuous activation function(AF). Under some criteria, CGNNs with this AF are shown to possess at least 5^(n)EPs, of which 3^(n)EPs are locally μ-stable. Compared with the saturated AF or the sigmoidal AF, CGNNs with the designed AF can produce many more total/stable EPs. Therefore, when CGNNs with the designed discontinuous AF are applied to associative memory, they can store more prototype patterns. Moreover, the AF is expanded to a more general version to further increase the number of total/stable equilibria. The CGNNs with the expanded AF are found to produce(2k+3)^(n)EPs, of which (k+2)^(n)EPs are locally μ-stable. By adjusting two parameters in the AF, the number of sufficient conditions ensuring the μ-stability of multiple equilibria can be decreased. This finding implies that the computational complexity can be greatly reduced.Two numerical examples and an application to associative memory are illustrated to verify the correctness of the obtained results.

关键词： associative memory Cohen-Grossberg neural networks discontinuous activation functions multiple equilibria μ-stability

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Stability and attractive basins of multiple equilibria in delayed two-neuron networks

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Chinese Physics B 2012年第7期21卷 216-223页

作者：黄玉娇张化光王占山 College of Information Science and Engineering Northeastern University

multiple stability for two-dimensional delayed recurrent neural networks with piecewise linear activation flmctions of 2r （r 〉 1） corner points is studied. Sufficient conditions are established for checking the existence of （2r ＋ 1）2 equilibria in delayed recurrent neural networks. Under these conditions, （r ＋ 1）2 equilibria are locally exponentially stable, and （2r＋ 1）2 -（r ＋ 1）2 -r2 equilibria are unstable. Attractive basins of stable equilibria are estimated, which are larger than invariant sets derived by decomposing state space. One example is provided to illustrate the effectiveness of our results.

关键词： delayed recurrent neural network multiple equilibria stability attractive basin

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Exploring multiple equilibria for symmetric 2×2 CES/LES pure exchange economies

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Applied Mathematics(A Journal of Chinese Universities) 2010年第2期25卷 137-154页

作者： SHI Xiao-jun ZHANG Shun-ming School of Economics and Management Beijing University of Aeronautics and Astronautics Beijing 100191 China China Financial Policy Research Center Renmin University of China Beijing 100872 China

This paper explores the existence of 3 equilibria for symmetric 2-individual 2-good CES/LES pure exchange economies. For certain parameterizations in the economies, we show analytically that there are no more than 3 equilibria. We generalize our analytical results of existence of 3 equilibria for a wide range of parameterizations. Then we provide examples of 3 equilibria and parameter zones of 3 equilibria for CES and CES/LES economies.

关键词： multiple equilibria Cobb-Douglas utility function CES/LES utility function.

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multiple equilibria in SSN Metabolic Module

Multiple Equilibria in SSN Metabolic Module

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第二十九届中国控制会议

作者： LEI Hong-Bo1,ZHANG Ji-Feng1,CHEN Luonan2 1.Key Laboratory of Systems and Control,Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China2.Department of Electrical Engineering and Electronics,Osaka Sangyo University,Osaka 574-8530,Japan

In this paper,a novel modeling framework based on network modularization decomposition is proposed to analyze the multi-stability of metabolic networks.We first decompose a metabolic network into four types of elementary modules according to the special structures of metabolic systems,and then focus on one key type of these modules-the single substrate and single product with no inhibition(SSN)module,by deriving a nonlinear ordinary differential equation(ODE)model based on the Hill kinetics.We show that the injectivity of the vector field of the ODE model is equivalent to the nonsingularity of the Jacobian matrix of this vector field,which enables us equivalently to convert an unverifiable sufficient condition on the absence of multiple equilibria of an SSN module into a verifiable one.Moreover,we prove that this sufficient condition is held when the SSN module has both input and output nodes.Such a theoretical result not only provides a general framework for modeling an SSN metabolic module,but also implies that if a biological system can be exactly modeled by an SSN module,then it cannot admit multiple equilibria(or steady states).

关键词： Metabolic Network multiple equilibria SSN Module

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Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

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Chinese Physics B 2022年第1期31卷 170-178页

作者：李月陈增强王增会仓诗建 College of Artificial Intelligence Nankai UniversityTianjin 300350China Department of Electrical and Mining Engineering University of South AfricaFlorida 1710South Africa Department of Product Design Tianjin University of Science and TechnologyTianjin 300222China

The thermostatted system is a conservative system different from Hamiltonian systems,and has attracted much attention because of its rich and different nonlinear dynamics.We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system.It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian,such as isosurfaces and local centers,and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions,while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian.Moreover,the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes,which are the segments of equilibrium curves of the generalized thermostatted system.Furthermore,the interesting results are vividly demonstrated by the numerical simulations.

关键词： multiple equilibria curve axes invariant tori cluster-shaped conservative chaos

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CONSTRUCTING EXAMPLES WITH 5 equilibria FOR SYMMETRIC 3×2 CES /LES PURE EXCHANGE ECONOMIES

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Acta Mathematica Scientia 2012年第6期32卷 2411-2430页

作者：黄慧石晓军张顺明 Faculty of Business University of ReginaReginaSaskatchewanS4S 0A2Canada China Financial Policy Research Center Renmin University of China

This paper explores the existence of multiple equilibria for symmetric 3 indi- vidual, 2 good CES / LES pure exchange economies. Analytically, we show that there are no more than 5 equilibria in such economies. The number of equilibria varies from 5 to 3 then to 1. We generalize our analytical results of existence of 1, 3, 5 equilibria for a wide range of parametrizations. We also provide concrete examples of 1, 3, 5 equilibria with parameter zones specified.

关键词： multiple equilibria CES / LES utility function

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Two-Dimensional Energy Balance Model and Its Application to Some Climatic Issues

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Journal of Meteorological Research 2014年第5期28卷 747-761页

作者：李耀锟巢纪平 College of Global Change and Earth System Science Beijing Normal University National Marine Environmental Forecasting Center

Based on a two-dimensional energy balance model, the studies on some climatic issues such as the re- lationship between ice cap latitude and solar constant, desertifieation, and the warming effect of carbon dioxide, have been reviewed and discussed. The phenomenon that a fixed solar constant might correspond to different equilibrium ice cap latitudes is determined by the continuity of albedo distribution. The disconti- nuity in albedo distribution increases the number of equilibrium ice cap latitudes. Desert would expand both northward and southward when desert surface albedo is increasing. This would deteriorate the ecological environment in border regions, and then threaten the existence of local inhabitants. Melting of the polar ice would not be accelerated, with increasing carbon dioxide concentration. The ice cap latitude would move northward slowly, with some “hiatus” periods, under the slowly increasing global average surface tempera- ture. According to the current research, future development of the two-dimensional energy balance model and possible progress are also forecasted.

关键词： two-dimensional energy balance model multiple equilibria ice cap latitude desertification warming effect of carbon dioxide

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EFFECTS OF MOIST PROCESS ON SUBTROPICAL FLOW PATTERNS AND multiple EQUILIBRIUM STATES

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Science China Chemistry 1988年第11期31卷 1352-1361页

作者：李麦村罗哲贤 Beijing Academia Sinica Lanzhou Meteorological Institute of Gansu Province Institute of Atmospheric Physics

A low-order general circulation moisture model is presented, and some experiments with it are described. The model is based on the quasi-geostrophic motion in the β-plane of two layers with landsea distribution. As proposed by Lorenz, the moisture variable in the model is the total dewpoint. Modeled processes consist of evaporation, precipitation, and the effects of clouds and water vapor on radiation.Results of the experiments with the model show that the moisture process enhances subtropical highs significantly and the meridional development of flow. It can also reproduce the hi-equilibrium states in certain parametric combinations, which is similar to the observational fact about the "Eastern pattern" and the "Western pattern" circulations in the subtropical areas during the summer half year.

关键词： moist low order model multiple equilibria low frequency oacillation.

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Fold Bifurcation Caused by Pollution Emission in an OLG Economy

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Journal of Systems Science and Information 2017年第4期8卷 302-309页

作者： Dong CAO Lin WANG Shouyang WANG School of Economics and Management Xidian University Academy of Mathematics and Systems Science China Academy of Sciences Department of Mathematics and Statistics University of New Brunswick

The purpose of this paper is to investigate the macroeconomic effect of pollution emission in an overlapping generation system. This is done through constructing an endogenous economy which generates pollution and environment deterioration. It shows how different level of pollution emission could cause complexity such as fold bifurcation in this system. In addition, numerical simulations are provided to show the emergency of complexity.

关键词： nonlinear pollution accumulation OLG model multiple equilibria fold bifurcation

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