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

Kuo-Shou Chiu
2013 Abstract and Applied Analysis  
The model 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).  ... 
doi:10.1155/2013/196139 fatcat:jd5etvcnpfcn5d6qtbbobfx4f4

The entropy concept for non-equilibrium states

E. H. Lieb, J. Yngvason
2013 Proceedings of the Royal Society A  
More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all 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.  ... 
doi:10.1098/rspa.2013.0408 pmid:24101892 pmcid:PMC3780809 fatcat:n2fmugzwljdodoe6kctk3gaq2i

A New Method of Lyapunov Functionals for Delayed Cellular Neural Networks

X. Li, L. Huang, J. Wu
2004 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
In this paper, we show that for 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.  ... 
doi:10.1109/tcsi.2004.836847 fatcat:gplt67zx2fffpjrdo5ujrjvy5y

On equilibria, stability, and instability of Hopfield neural networks

Zhi-Hong Guan, G. Chen, Yi Qin
2000 IEEE Transactions on Neural Networks  
Existence and 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.  ... 
doi:10.1109/72.839023 pmid:18249783 fatcat:ajfvmjwebjejdhxq74eiyv7bki

Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Xiaohui Xu, Jiye Zhang, Quan Xu, Zilong Chen, Weifan Zheng
2017 Complexity  
Firstly, the existence and 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( − )  ... 
doi:10.1155/2017/3826729 fatcat:bndisvvlabbmpp3li4b2oi43da

An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays

Zeynep Orman, Sabri Arik
2013 Abstract and Applied Analysis  
stability of the 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  ... 
doi:10.1155/2013/143585 fatcat:on5cthgumzh4lnjw3mzo7bzdme

On the use of "small external fields" in the problem of symmetry breakdown in statistical mechanics

David Ruelle
1972 Annals of Physics  
We study the infinite 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].  ... 
doi:10.1016/0003-4916(72)90181-9 fatcat:tqqiq746ivbrllclf6hvzb27cu

Solubility and critical phenomena in reactive liquid–liquid systems

Alexander Toikka, Maria Toikka
2009 Pure and Applied Chemistry  
The special aim is to consider the critical 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).  ... 
doi:10.1351/pac-con-08-11-04 fatcat:tcfwlwindjdc5bk2q745zzrwp4

A reference model approach to stability analysis of neural networks

Hong Qiao, Jigen Peng, Zong-Ben Xu, Bo Zhang
2003 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
The core of the new approach is to study a neural network model 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 .  ... 
doi:10.1109/tsmcb.2002.804368 pmid:18238244 fatcat:ur47k5enizasjgs4wmhd6lbqca

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

M. De la Sen, R. Nistal, S. Alonso-Quesada, A. Ibeas
2019 Discrete Dynamics in Nature and Society  
Those auxiliary 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.  ... 
doi:10.1155/2019/8959681 fatcat:xduj3omfe5atreof46nfw5jtai

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.  ... 

INSTANTANEOUS AND NON-INSTANTANEOUS ADJUSTMENT TO EQUILIBRIUM IN TWO-SECTOR GROWTH MODELS(*)

Antonio Bosch, Andreu Mas-Colell, Assaf Razin
1973 Metroeconomica  
(u,t) = x is a steady-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  ... 
doi:10.1111/j.1467-999x.1973.tb00203.x fatcat:hahlvxanjrharetyfasfo4ubny

From local to global equilibrium states: Thermodynamic formalism via an inducing scheme

Renaud Leplaideur
2014 Electronic Research Announcements in Mathematical Sciences  
We present a method to construct 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  ... 
doi:10.3934/era.2014.21.72 fatcat:64ntvc23njc4xcjvitcbb2lzki

Some Properties of The Solution of The Ramsey Model

Ioana Viaşu
2014 Timisoara Journal of Economics and Business  
reaches the 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.  ... 
doi:10.1515/tjeb-2015-0006 fatcat:mjhcayotkbaovekxlwgfj7eu64

Virial equilibrium states of spheroidal stellar systems

Y. N. Fu, Y. S. Sun
1999 Monthly notices of the Royal Astronomical Society  
In this paper, we present virial 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.  ... 
doi:10.1046/j.1365-8711.1999.02290.x fatcat:ejnejor3gnfxddfcept762jtr4
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