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Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument

2013
*
Abstract and Applied Analysis
*

The model

doi:10.1155/2013/196139
fatcat:jd5etvcnpfcn5d6qtbbobfx4f4
*with*the advanced argument is*system**with*strong anticipation.*Some*sufficient conditions are established for the existence and global exponential stability of a*unique**equilibrium*. ... We introduce impulsive cellular neural network models*with*piecewise alternately advanced and retarded argument (in short IDEPCA). ... Then there exists a*unique**equilibrium**state** of the ICNNs*with*IDEPCA*system*(5a)-(5b). ...##
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The entropy concept for non-equilibrium states

2013
*
Proceedings of the Royal Society A
*

More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all

doi:10.1098/rspa.2013.0408
pmid:24101892
pmcid:PMC3780809
fatcat:n2fmugzwljdodoe6kctk3gaq2i
*equilibrium**states*of all*systems*that has the appropriate additivity and scaling properties ... The concept of comparability of*states**with*respect to adiabatic changes plays an important role in our reasoning. ... To formulate and discuss this question precisely, we consider a*system**with*a space Γ of*equilibrium**states*that is embedded as a subset in*some*larger spaceΓ of non-*equilibrium**states*. ...##
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A New Method of Lyapunov Functionals for Delayed Cellular Neural Networks

2004
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IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
*

In this paper, we show that for

doi:10.1109/tcsi.2004.836847
fatcat:gplt67zx2fffpjrdo5ujrjvy5y
*some*delay differential*systems*such as additive neural networks*with*delays, we can weaken the condition that the Lyapunov functional or function is positive definite, ... Lyapunov functionals and Lyapunov functions coupled*with*the Razumikhin technique are still the most popular tools in studying the stability of large-scale retarded nonlinear*systems*. ... But, the conditions of Corollary 4 in this paper are satisfied*with*, and*system*(15) has a*unique*and globally exponentially stable*equilibrium*. ...##
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On equilibria, stability, and instability of Hopfield neural networks

2000
*
IEEE Transactions on Neural Networks
*

Existence and

doi:10.1109/72.839023
pmid:18249783
fatcat:ajfvmjwebjejdhxq74eiyv7bki
*uniqueness*of*equilibrium*, as well as its stability and instability, of a continuous-time Hopfield neural network are studied. A set of new and simple sufficient conditions are derived. ... CONCLUSIONS*Some*new and simple sufficient conditions for the existence,*uniqueness*, stability, and instability of the*equilibrium**state*of a continuous-time Hopfield neural network have been derived in ... In addition, if condition 2) or 4) of Theorem 1 holds then (17) has a*unique*unstable*equilibrium**state*. ...##
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Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

2017
*
Complexity
*

Firstly, the existence and

doi:10.1155/2017/3826729
fatcat:bndisvvlabbmpp3li4b2oi43da
*uniqueness*of the*equilibrium*point of the*system*are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. ... The obtained results in this paper are*with*a lower level of conservatism in comparison*with**some*existing ones. ... To sum up, it can be concluded from Steps 1 and 2 that*system*(1) has a*unique**equilibrium*point z # , and the*equilibrium*point is globally exponentially stable*with*exponential converge rate 0.5( − ) ...##
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An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays

2013
*
Abstract and Applied Analysis
*

stability of the

doi:10.1155/2013/143585
fatcat:on5cthgumzh4lnjw3mzo7bzdme
*equilibrium*point for this class of neutral-type*systems*. ... The problem of existence,*uniqueness*, and global asymptotic stability is considered for the class of neutral-type neural network model*with*discrete time delays. ... Conclusions In this paper, we have obtained*some*sufficient conditions for the existence,*uniqueness*, and global asymptotic stability of the*equilibrium*point for the class of neutral-type*systems**with*...##
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On the use of "small external fields" in the problem of symmetry breakdown in statistical mechanics

1972
*
Annals of Physics
*

We study the infinite

doi:10.1016/0003-4916(72)90181-9
fatcat:tqqiq746ivbrllclf6hvzb27cu
*system**equilibrium**states*in the statistical mechanics of classical lattice gases. ... In an appendix we show that an Ising ferromagnet in a nonvanishing magnetic field has only one*equilibrium**state*. ... If there is only one invariant*equilibrium**state*p, let pP be the*unique*measure*with*resultant p carried by the extremal*equilibrium**states*[S]. ...##
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Solubility and critical phenomena in reactive liquid–liquid systems

2009
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Pure and Applied Chemistry
*

The special aim is to consider the critical

doi:10.1351/pac-con-08-11-04
fatcat:tcfwlwindjdc5bk2q745zzrwp4
*states*in these*systems*. The reactive liquid–liquid*equilibrium*(LLE) is treated on the base of phase rule. ... The topology of diagrams of reactive LLE is discussed for*some*types of binary and ternary*systems*. ...*system**with*intersection of chemical*equilibrium*curve and binodal: case of one*unique*reactive tie-line (dotted line). ...##
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A reference model approach to stability analysis of neural networks

2003
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IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)
*

The core of the new approach is to study a neural network model

doi:10.1109/tsmcb.2002.804368
pmid:18238244
fatcat:ur47k5enizasjgs4wmhd6lbqca
*with*reference to other related models, so that different modeling approaches can be combinatively used and powerfully cross-fertilized. ... Focused on two representative neural network modeling approaches (the neuron*state*modeling approach and the local field modeling approach), we establish a rigorous theoretical basis on the feasibility ... In the following lemmas we summarize the basic stability results of*system*(4 , . Then,*system*(4) has a*unique**equilibrium**state*. ...##
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Some Formal Results on Positivity, Stability, and Endemic Steady-State Attainability Based on Linear Algebraic Tools for a Class of Epidemic Models with Eventual Incommensurate Delays

2019
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Discrete Dynamics in Nature and Society
*

Those auxiliary

doi:10.1155/2019/8959681
fatcat:xduj3omfe5atreof46nfw5jtai
*systems*are used to formulate stability and positivity properties independently of the delay sizes.*Some*examples are discussed to the light of the developed formal study. ... Two auxiliary delay-free*systems*are defined related to the linearization processes around the*equilibrium*points which correspond to the zero delay, i.e., delay-free, and infinity delay cases. ...*Some*conditions are also given for the*uniqueness*of the endemic*equilibrium*point in Theorem B.2 of Appendix B based on the Rouché-Frobenius test for compatibility of solutions in algebraic*systems*. ...##
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Page 35 of American Anthropologist Vol. 90, Issue 2
[page]

1988
*
American Anthropologist
*

In a

*system**with*a*unique*stable*state*the*system*will always return to the*equilibrium*value regardless of the initial set of conditions or any pertur- bation to the*system*. ... As is clear from the above discussion, a*system*may have only one*equilibrium*point or several*equilibrium*points,*some*stable and*some*unstable. ...##
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INSTANTANEOUS AND NON-INSTANTANEOUS ADJUSTMENT TO EQUILIBRIUM IN TWO-SECTOR GROWTH MODELS(*)

1973
*
Metroeconomica
*

(u,t) = x is a steady-

doi:10.1111/j.1467-999x.1973.tb00203.x
fatcat:hahlvxanjrharetyfasfo4ubny
*state**equilibrium*of the*system*(26) - (31) . Suppose that at x = (u,i) , u = o. ... (m,k) --for short x --is a steady*state*of the*system*. ... B) Classical Savings Assumption The*uniquely*determined momentary*equilibrium*is given by f~ = pf~ Equations ( 52 ) -(53) reduce to (56) Let k (w) be the*uniquely*determined capital-labor ratio corresponding ...##
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From local to global equilibrium states: Thermodynamic formalism via an inducing scheme

2014
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Electronic Research Announcements in Mathematical Sciences
*

We present a method to construct

doi:10.3934/era.2014.21.72
fatcat:64ntvc23njc4xcjvitcbb2lzki
*equilibrium**states*via inducing. This method can be used for*some*non-uniformly hyperbolic dynamical*systems*and for non-Hölder continuous potentials. ... The existence of*equilibrium**states*for less regular potentials and/or for*systems**with*weaker hyperbolicity properties is a challenging task. ... lim Z→Zc log λ Z < 0, -or lim Z→Zc log λ Z = 0 and lim Z→Zc L(τ ) = +∞. • If there is one global*equilibrium**state*µ such that µ(R) > 0, then, it is the*unique**equilibrium**state**with*full support, if ...##
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Some Properties of The Solution of The Ramsey Model

2014
*
Timisoara Journal of Economics and Business
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reaches the

doi:10.1515/tjeb-2015-0006
fatcat:mjhcayotkbaovekxlwgfj7eu64
*unique*steady-*state**equilibrium*, for any starting values of per-capita consumption. ... Our approach clarifies why different starting values of per-capita consumption generates the same steady-*state**equilibrium*, but of different periods of time. ... Now it is clear that the*system*reaches the*unique*steady-*state**equilibrium*for any starting point c0. ...##
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Virial equilibrium states of spheroidal stellar systems

1999
*
Monthly notices of the Royal Astronomical Society
*

In this paper, we present virial

doi:10.1046/j.1365-8711.1999.02290.x
fatcat:ejnejor3gnfxddfcept762jtr4
*equilibrium**states*of spheroidal stellar*systems*and study their linear stability. ... For each a, there exists a*unique**equilibrium**state*that is linearly stable under our assumptions. The*equilibrium*con®guration is prolate, spherical and oblate if a < 1, a 1 and a > 1, respectively. ... For any given a, there exists a*unique**equilibrium**state*of spheroidal stellar*systems*. The*equilibrium*con®guration is spherical when a 1, oblate when a > 1 and prolate when a < 1. ...
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