A SUFFICIENT CONDITION FOR THE EXISTENCE OF A UNIQUE EQUILIBRIUM STATE IN AN ADIABATIC TUBULAR REACTOR

AbstractIn this paper we consider horseshoes with homoclinic tangencies inside the limit set. For a class of such maps, we prove the existence of a unique equilibrium state μt, associated to the (non-continuous) potential −tlog Ju. We also prove that the Hausdorff dimension of the limit set, in any open piece of unstable manifold, is the unique number t0 such that the pressure of μt0 is zero. To deal with the discontinuity of the jacobian, we introduce a countable Markov partition adapted to the dynamics, and work with the first return map defined in a rectangle of it.

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Entropy approximation versus uniqueness of equilibrium for a dense affine space of continuous functions

Stochastics and Dynamics ◽

10.1142/s0219493716500209 ◽

2016 ◽

Vol 16 (06) ◽

pp. 1650020

Author(s):

Henri Comman

Keyword(s):

Invariant Measure ◽

Equilibrium State ◽

Affine Space ◽

Continuous Functions ◽

Metrizable Space ◽

Unique Equilibrium ◽

Space Of Continuous Functions ◽

Compact Metrizable Space ◽

Uniqueness Of Equilibrium ◽

Unique Equilibrium State

We show that for a [Formula: see text]-action (or [Formula: see text]-action) on a non-empty compact metrizable space [Formula: see text], the existence of a affine space dense in the set of continuous functions on [Formula: see text] constituted by elements admitting a unique equilibrium state implies that each invariant measure can be approximated weakly[Formula: see text] and in entropy by a sequence of measures which are unique equilibrium states.

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On the Unique Equilibrium State of Tetraploids under Selection

Biometrics ◽

10.2307/2532910 ◽

1996 ◽

Vol 52 (2) ◽

pp. 717 ◽

Cited By ~ 1

Author(s):

M. K. Singh ◽

Ram A. Kumar

Keyword(s):

Equilibrium State ◽

Unique Equilibrium ◽

Unique Equilibrium State

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On stability of stratified elastic geosystems in a gravity field

Доклады Академии наук ◽

10.31857/s0869-56524893298-302 ◽

2019 ◽

Vol 489 (3) ◽

pp. 298-302

Author(s):

E. I. Ryzhak ◽

S. V. Sinyukhina

Keyword(s):

Equilibrium State ◽

Gravity Field ◽

Stability Condition ◽

Shear Stiffness ◽

Density Increase ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Stabilizing Effect ◽

Necessary And Sufficient

Stability of stratified elastic geosystems in a gravity field is studied analytically with regard for the shear stiffness of geomaterial. A sufficient condition for stability of a geomass clamped at the lateral boundaries, is obtained: for any ratios of dimensions of the geomass it is sufficient for stability that the rate of density increase with depth (in the loaded equilibrium state) exceed a certain positive value which depends on shear stiffness so that the greater the stiffness, the less the value, and vice versa (the stabilizing effect of shear stiffness). At zero shear stiffness the value mentioned is maximal and characterizes the necessary and sufficient condition for stability of a bulk-elastic geomass. Geophysical consequences of obtained stability condition are analyzed.

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Entry-Proofness and Discriminatory Pricing under Adverse Selection

The American Economic Review ◽

10.1257/aer.20190189 ◽

2021 ◽

Vol 111 (8) ◽

pp. 2623-2659

Author(s):

Andrea Attar ◽

Thomas Mariotti ◽

François Salanié

Keyword(s):

Adverse Selection ◽

Sufficient Condition ◽

Unique Equilibrium ◽

Necessary And Sufficient Condition ◽

Recursive Structure ◽

Equilibrium Outcome ◽

Balanced Allocation ◽

Necessary And Sufficient

This paper studies competitive allocations under adverse selection. We first provide a general necessary and sufficient condition for entry on an inactive market to be unprofitable. We then use this result to characterize, for an active market, a unique budget-balanced allocation implemented by a market tariff making additional trades with an entrant unprofitable. Motivated by the recursive structure of this allocation, we finally show that it emerges as the essentially unique equilibrium outcome of a discriminatory ascending auction. These results yield sharp predictions for competitive nonexclusive markets. (JEL D11, D43, D82, D86)

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Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs

Discrete Dynamics in Nature and Society ◽

10.1155/2017/3540278 ◽

2017 ◽

Vol 2017 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Youness El Ansari ◽

Ali El Myr ◽

Lahcen Omari

Keyword(s):

Equilibrium State ◽

Stationary Distribution ◽

Computer Network ◽

Reproduction Number ◽

Sufficient Condition ◽

Stochastic Perturbations ◽

Stochastic Fluctuations ◽

Spread Model ◽

The Stability ◽

Theoretical Results

We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero). The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results.

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A necessary and sufficient condition for a matrix equilibrium state to be mixing

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2017.122 ◽

2017 ◽

Vol 39 (8) ◽

pp. 2223-2234 ◽

Cited By ~ 2

Author(s):

IAN D. MORRIS

Keyword(s):

Equilibrium State ◽

Sufficient Conditions ◽

Equilibrium States ◽

Necessary And Sufficient Conditions ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Hölder Continuous ◽

Ergodic Properties ◽

Bernoulli Measure ◽

Necessary And Sufficient

Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to Hölder-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more recent, with a complete description of such equilibrium states being achieved by Feng and Käenmäki [Equilibrium states of the pressure function for products of matrices.Discrete Contin. Dyn. Syst.30(3) (2011), 699–708]. In a recent article [Ergodic properties of matrix equilibrium states.Ergod. Th. & Dynam. Sys.(2017), to appear] the author investigated the ergodic-theoretic properties of these matrix equilibrium states, attempting in particular to give necessary and sufficient conditions for mixing, positive entropy, and the property of being a Bernoulli measure with respect to the natural partition, in terms of the algebraic properties of the semigroup generated by the matrices. Necessary and sufficient conditions were successfully established for the latter two properties, but only a sufficient condition for mixing was given. The purpose of this note is to complete that investigation by giving a necessary and sufficient condition for a matrix equilibrium state to be mixing.

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NOVEL STABILITY CRITERIA FOR DELAYED CELLULAR NEURAL NETWORKS

International Journal of Neural Systems ◽

10.1142/s0129065703001649 ◽

2003 ◽

Vol 13 (05) ◽

pp. 367-375 ◽

Cited By ~ 24

Author(s):

JINDE CAO ◽

JUN WANG ◽

XIAOFENG LIAO

Keyword(s):

Neural Networks ◽

Asymptotic Stability ◽

Global Asymptotic Stability ◽

Lyapunov Method ◽

Equilibrium Points ◽

Cellular Neural Networks ◽

Sufficient Condition ◽

Unique Equilibrium ◽

Stability Criteria ◽

Output Stability

In this paper, a new sufficient condition is given for the global asymptotic stability and global exponential output stability of a unique equilibrium points of delayed cellular neural networks (DCNNs) by using Lyapunov method. This condition imposes constraints on the feedback matrices and delayed feedback matrices of DCNNs and is independent of the delay. The obtained results extend and improve upon those in the earlier literature, and this condition is also less restrictive than those given in the earlier references. Two examples compared with the previous results in the literatures are presented and a simulation result is also given.

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Bidding Behavior and Equilibrium Excursion of Uniform Price Auction Mechanism

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595917500282 ◽

2017 ◽

Vol 34 (06) ◽

pp. 1750028 ◽

Cited By ~ 1

Author(s):

Congjun Rao ◽

Yong Zhao ◽

Junjun Zheng ◽

Mark Goh ◽

Cheng Wang

Keyword(s):

Multiple Equilibria ◽

Unique Equilibrium ◽

Uniform Price Auction ◽

Bidding Behavior ◽

Uniform Price ◽

Auction Mechanism ◽

Common Value ◽

Price Auction ◽

The Relationship ◽

Unique Equilibrium State

Multiple equilibria (equilibrium excursion) affects the auction proceeds, and is bad for estimating auction efficiency. This paper examines the relationship between bidding behavior and equilibrium excursion. We analyze a uniform price auction mechanism based on a rationing strategy and common value information. In this uniform price auction mechanism, bidders (strategic and non-strategic) participate in an auction simultaneously, and the auctioneer rations the strategic bidders after observing their bids. The conclusions drawn suggest that a rationing strategy can effectively limit the strategic bidders from manipulating the auction, and the Nash equilibrium may not be unique (i.e., there exists an equilibrium excursion). As the number of bidders increases, or when the quantity that can be allocated to the non-strategic bidders is unconstrained, there exists asymptotically a unique equilibrium price which is the highest price the auctioneer could obtain. Based on these conclusions, we provide some strategies and suggestions on how to induce the equilibrium excursion state to a desired unique equilibrium state.

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