Kinds Of Equilibria Research Articles

Evolution of current- and pressure-driven instabilities in relativistic jets

ABSTRACT Instabilities in relativistic magnetized jets are thought to be deeply connected to their energy dissipation properties and to the consequent acceleration of the non-thermal emitting relativistic particles. Instabilities lead to the development of small-scale dissipative structures, in which magnetic energy is converted in other forms. In this paper we present three-dimensional numerical simulations of the instability evolution in highly magnetized plasma columns, considering different kinds of equilibria. In fact, the hoop stresses related to the azimuthal component of magnetic field can be balanced either by the magnetic pressure gradient (force-free equilibria, FF) or by the thermal pressure gradient (pressure-balanced equilibria, PB) or by a combination of the two. FF equilibria are prone to current-driven instabilities (CDI), while PB equilibria are prone to pressure-driven instabilities (PDI). We perform a global linear stability analysis, from which we derive the different instability properties in the two regimes, showing that PDI have larger growth rates and are also unstable for high wavenumbers. The numerical simulations of the non-linear instability evolution show similar phases of evolution in which the formation of strong current sheets is followed by a turbulent quasi-steady state. PDI are however characterized by a faster evolution, by the formation of smaller scale dissipative structures and larger magnetic energy dissipation.

From General Equilibrium to Algorithmic Equilibrium

Based on the Algorithmic Thinking Theory, this essay introduces the concept of “Algorithmic Equilibrium”, which can really exist and be used to replace, re-interpret, and/or synthesize all other kinds of equilibria, and to allow the coexistence of equilibria and various dis-equilibria in a unified, dynamic, and developmental panorama, thus exhibiting a grand synthesis of economics.

From General Equilibrium to Algorithmic Equilibrium

Based on the Algorithmic Thinking Theory, this essay introduces the concept of “Algorithmic Equilibrium”, which can really exist and be used to replace, re-interpret, and/or synthesize all other kinds of equilibria, and to allow the coexistence of equilibria and various dis-equilibria in a unified, dynamic, and developmental panorama, thus exhibiting a grand synthesis of economics.

Analysis and simulation of a delayed HIV model with reaction–diffusion and sliding control

Selection of an appropriate therapy threshold to restrain the virus load is still challenging on structured treatment interruptions (STIs) for HIV. In this paper, we ponder that how the sliding control and multistability to regulate the treatment effect through comprehensive dynamics of a virus-immune model. Firstly, based on piecewise therapy, we propose a delayed reaction–diffusion virus-immune model under the homogeneous Neumann boundary condition. Secondly, the existence and stabilities of five kinds of equilibria as well as the direction and stability of spatial Hopf bifurcation at regular equilibrium are investigated. Thirdly, the sliding domain and the boundary node bifurcations are addressed by theoretical analysis. Finally, we appraise the effects of therapy threshold, sliding domain and multistability on HIV therapy by simulations, and further seek out the appropriate therapy threshold for infected patients with given physiological parameters and present the corresponding principles. Our explorations will provide evidence for HIV and other disease therapies.

Stability analysis and optimal control in an epidemic model on directed complex networks with nonlinear incidence

In this paper, stability and optimal control for SIS epidemic systems with birth and death in directed complex networks are investigated. A class of epidemic systems are constructed based on SIS models combining with two kinds of topological characters as in-degree and out-degree in directed networks, in which the nonlinear incidence rate is introduced that relevant to network’s topology containing the psychological effect coefficient. The disease-free and the endemic equilibria are derived and the epidemic threshold for our systems is obtained. Then, the local stability about the disease-free and the endemic equilibria are discussed via the corresponding Jacobian matrices and the characteristic equation. In addition, global asymptotical stability about two kinds of equilibria are also considered based on the Lyapunov function and stable analysis method. From the view of Pontryagin Minimum Principle, the optimal control issue about the system is also considered, and the corresponding optimal control systems and optimal control tactics are obtained. Several numerical examples are provided to demonstrate the effectiveness of our main method. Meanwhile, by means of the Forward–Backward Sweep method, optimal control systems are solved in the aspect of numeric and the control aim under the derived strategies is achieved.

Depinning transition of travelling waves for particle chains

In this paper we apply Aubry–Mather theory for equilibria of 1D Hamiltonian lattice systems and the theory of invariant ordered circles to investigate the depinning transition of travelling waves for particle chains. Assume A < B are two critical values such that the particle chain has three homogeneous equilibria if the driving force . It is already known that there exist transition thresholds of the driving force such that the particle chain has stationary fronts but no travelling fronts for and travelling fronts but no stationary fronts if or . The novelty of our approach is that we prove the transition threshold () coincides with the upper (lower) limit of the upper (lower) depinning force as the rotation number tends to zero from the right. Based on this conclusion, we demonstrate that when the driving force , besides stationary fronts there are various kinds of equilibria with rotation numbers close to zero such that the spatial shift map has positive topological entropy on the set of equilibria. Furthermore, we give a necessary and sufficient condition for the absence of propagation failure, i.e. , in terms of a minimal foliation. Finally we show that are continuous with respect to potential functions in C 1 topology.

Dynamical aspects of pine wilt disease and control measures

Abstract In this paper, we have inquired pine wilt disease (PWD) governed by a mathematical model to access its dynamics. By using next generation matrix method, we worked out for basic reproduction number R ∘ , which apprises us about the disease dissemination or control in the community. Two kinds of equilibria, disease absent and disease present, have been established. Stability of both equilibria has been discussed. Lypunove functional theory and graph theoretic approach are used for disease free and endemic equilibrium, respectively. The parameters, expressed in the model, captured the growth in case onsets and the estimated results are almost compatible with the studied actual reported cases. By using the estimated parameters, we found the sensitivity indices of the basic reproduction number through the calculation of ratio of relative change in the parameter to the relative change in R ∘ . Influence of the parameters on the number of infectious pines and bark beetles has also been observed by the variation of parameters. Keeping in mind those vital factors, calculated through sensitivity analysis, that can help to overcome the disease, an effective control strategy has been designed and optimal control problem has been formulated. To get in sight the comparison of analytical results with numerical ones, the problem has been reconsidered, and it has been seen that numerical results, obtained by using estimated parameters, express effectiveness of the applied controls to reduce pine wilt infection.

Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1

Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point (+∞,0) or (0,+∞) in each region depending on nonnegative initial conditions. These results completely described the behavior of the system.

Workplace Deviance and Recession

AbstractWe examine the relationship between the incidence of workplace deviance (on-the-job crime) and the state of the economy. A worker’s probability of future employment depends on whether she has been deviant as well as on the availability of jobs. Using a two period model we show that the net impact on deviant behavior to changes in unemployment can go either way depending upon the nature of the equilibrium. Two kinds of equilibria are possible. In one, a non-deviant’s probability of being employed increases as expected market conditions improve which lowers the incentive to be a deviant. In contrast, in the other kind of equilibrium, the deviant’s probability of being employed increases when market conditions improve which increases the incentive to be a deviant. In either case, there is a setup cost to deviant behavior and the attractiveness of incurring that increases with an increase in expected probability of future employment which unambiguously increases the incentive to be deviant. In the first kind of equilibrium, the two effects counteract each other, while in the second they reinforce each other. Finally, we characterize conditions under which an increase in optimism, i.e. a reduction in the probability of facing a recession unambiguously increases deviant behavior.

Orbital dynamics and equilibrium points around an asteroid with gravitational orbit–attitude coupling perturbation

The strongly perturbed dynamical environment near asteroids has been a great challenge for the mission design. Besides the non-spherical gravity, solar radiation pressure, and solar tide, the orbital motion actually suffers from another perturbation caused by the gravitational orbit–attitude coupling of the spacecraft. This gravitational orbit–attitude coupling perturbation (GOACP) has its origin in the fact that the gravity acting on a non-spherical extended body, the real case of the spacecraft, is actually different from that acting on a point mass, the approximation of the spacecraft in the orbital dynamics. We intend to take into account GOACP besides the non-spherical gravity to improve the previous close-proximity orbital dynamics. GOACP depends on the spacecraft attitude, which is assumed to be controlled ideally with respect to the asteroid in this study. Then, we focus on the orbital motion perturbed by the non-spherical gravity and GOACP with the given attitude. This new orbital model can be called the attitude-restricted orbital dynamics, where restricted means that the orbital motion is studied as a restricted problem at a given attitude. In the present paper, equilibrium points of the attitude-restricted orbital dynamics in the second degree and order gravity field of a uniformly rotating asteroid are investigated. Two kinds of equilibria are obtained: on and off the asteroid equatorial principal axis. These equilibria are different from and more diverse than those in the classical orbital dynamics without GOACP. In the case of a large spacecraft, the off-axis equilibrium points can exist at an arbitrary longitude in the equatorial plane. These results are useful for close-proximity operations, such as the asteroid body-fixed hovering.

Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure

By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.

Signaling equilibria in sensorimotor interactions

Although complex forms of communication like human language are often assumed to have evolved out of more simple forms of sensorimotor signaling, less attention has been devoted to investigate the latter. Here, we study communicative sensorimotor behavior of humans in a two-person joint motor task where each player controls one dimension of a planar motion. We designed this joint task as a game where one player (the sender) possesses private information about a hidden target the other player (the receiver) wants to know about, and where the sender’s actions are costly signals that influence the receiver’s control strategy. We developed a game-theoretic model within the framework of signaling games to investigate whether subjects’ behavior could be adequately described by the corresponding equilibrium solutions. The model predicts both separating and pooling equilibria, in which signaling does and does not occur respectively. We observed both kinds of equilibria in subjects and found that, in line with model predictions, the propensity of signaling decreased with increasing signaling costs and decreasing uncertainty on the part of the receiver. Our study demonstrates that signaling games, which have previously been applied to economic decision-making and animal communication, provide a framework for human signaling behavior arising during sensorimotor interactions in continuous and dynamic environments.

Efficiency May Improve When Defectors Exist

Voluntarily Separable Repeated Prisoner's Dilemma (Fujiwara-Greve and Okuno-Fujiwara, 2009) has many kinds of equilibria. Focusing on monomorphic and bimorphic equilibria, we show that a bimorphic equilibrium consisting of cooperators and defectors is most efficient, under a mild payoff condition. This is a striking contrast to ordinary repeated Prisoner's Dilemma, where the symmetric efficient payoff is achieved by the symmetric C-trigger equilibrium. Our result indicates that behavioral diversity can be beneficial for the society, when players are free to escape from personalized punishments. Length: 34 pages

Workplace Deviance and Recession

We examine the relationship between the incidence of workplace deviance (on-the-job crime) and the state of the economy. A worker's probability of future employment depends on whether she has been deviant as well as on the availability of jobs. Using a two period model we show that the net impact on deviant behavior to changes in unemployment can go either way depending upon the nature of the equilibrium. Two kinds of equilibria are possible. In one, a non-deviant's probability of being employed increases as expected market conditions improve which lowers the incentive to be a deviant. In contrast, in the other kind of equilibrium, the deviant's probability of being employed increases when market conditions improve which increases the incentive to be a deviant. In either case, there is a setup cost to deviant behavior and the attractiveness of incurring that increases with an increase in expected probability of future employment which unambiguously increases the incentive to be deviant. In the first kind of equilibrium, the two effects counteract each other, while in the second they reinforce each other. Finally, we show that an increase in optimism, i.e. a reduction in the probability of facing a recession unambiguously increases deviant behavior.

Probabilistic Assignment: Implementation in Stochastic Dominance Nash Equilibria

We study the assignment of objects to people via lotteries based only on their ordinal preferences. In particular, we analyze the strategic implications of several natural assumptions regarding how people compare lotteries. These are that a person prefers a given lottery to: a) lotteries that it stochastically dominates with respect to his ordinal preferences, b) lotteries that do not stochastically dominate it with respect to his ordinal preferences, and c) lotteries that yield a lower expected utility for particular von Neumann-Morgenstern preferences consistent with his ordinal preferences. Corresponding to each assumption, we dene a version of Nash equilibrium. We identify a single mild (Maskin-style) invariance condition that is a necessary and sucient condition for implementability all three kinds of equilibria. Thus, we conclude that three types of implementability are equivalent. We show that when there are exactly three people there is only one Pareto-ecient and envy-free|in the stochastic dominance sense|rule that satises this condition: the probabilistic serial rule (Bogomolnaia and Moulin 2001). JEL classication : C71, D63

How to introduce temperature to the 1D Sznajd model

We investigate the possibility of introducing temperature to the one dimensional Sznajd model and propose a natural extension of the original model by including other types of interactions. We characterise different kinds of equilibria into which the extended system can evolve. We determine the consequences of fulfilling the detailed balance condition and we prove that in some cases it is equivalent to microscopic reversibility. We found the equivalence of the model to the standard (inflow) model with interactions up to next nearest neighbors. It is shown that under some constraints there exists a Hamiltonian compatible with the dynamics and its form resembles that of the 1D ANNNI model. It appears however, that the standard approach of constructing temperature from the Hamiltonian fails. In this situation we propose a simple definition of the temperature-like quantity that measures the size of fluctuations in the system at equilibrium. The complete list of zero-temperature degenerated cases as well as the list of ground states of the derived Hamiltonian are provided.

HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS

For the Lax KdV5 equation and the KdV–Sawada–Kotera–Ramani equation, their corresponding four-dimensional traveling wave systems are studied by using Congrove's method. Exact explicit gap soliton, embedded soliton, periodic and quasi-periodic wave solutions are obtained. The existence of homoclinic manifolds to three kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. The bifurcation conditions of equilibria are given.

Competitive Investment Strategies in New Technology Adoption with a Further New Technology Anticipated

This paper studies a general dynamic duopoly in which two firms compete in the adoption of current technology with a further new technology anticipated. Three kinds of equilibria may occur in technology adoption, namely the preemptive, sequential, and simultaneous equilibrium, depending on the level of operating costs and the first-move advantage. It shows that the faster technological innovation encourages the leader to invest earlier, while induces the follower to invest later. Furthermore, like the investment costs, with the increase of the operating costs, the follower tends to invest later, while the leader tends to invest earlier. However, the investment thresholds are more sensitive to the change of the operating costs than that of the investment costs.

Quasi-Competitive Cournot Oligopoly with Product Differentiation and Symmetric Firms

Since Vives (1984), Cheng (1985) and Okuguchi (1987), the equilibria in Bertrand and Cournot oligopolies with product differentiation have been known to differ. Okuguchi (2005) has shown that Bertrand priceadjusting oligopoly with product differentiation and symmetric firms is quasi-competitive but not perfectly competitive in the limit state of infinite number of firms. This paper formulates and analyzes two types of Cournot output-adjusting oligopoly with product differentiation and symmetric firms, in one of which symmetric firms producing the same goods are assumed to collude, and in the other, collusion is ruled out. The limit states are shown to be different in two oligopolies but they are both quasi-competitive. It is well known, since the seminal paper of Ruffin (1971), that the Cournot oligopoly without product differentiation and symmetric firms is quasi-competitive in the sense that the equilibrium industry output increases with an increase in the number of firms, and that the equilibrium product price converges to the competitive one under a set of reasonable conditions on the inverse market demand function and the firm’s cost function. Okuguchi (1973) has extended Ruffin’s result taking into account asymmetric firms and adapting the method of the proof of Debreu and Scarf (1963) of the equivalence of the core and the perfectly competitive equilibrium in the limit state of a pure exchange economy. Two kinds of equilibria are conceivable for Cournot oligopoly without product differentiation and with symmetric firms with identical cost functions. The first equilibrium emerges when all firms behave with a priori knowledge that their equilibrium outputs are the same. The second equilibrium occurs when all symmetric firms do not know in advance that their equilibrium outputs are identical. This is the case of non-collusion and was first systematically analyzed by Ruffin (1971). In section 2 we will analyze the differences between the two equilibria in Cournot oligopoly without product differentiation and with symmetric firms. The difference of the equilibria in Cournot oligopoly without product differentiation and with symmetric firms and with or without collusion was first suggested by Kemp and Shimomura (1995). We will find that the Cournot oligopoly equilibria are quasi-competitive but do not converge to a perfectly competitive equilibrium when the number of firms becomes infinite and when collusion exists. If oligopoly consists of firm producing differentiated products, the firm may choose price or output as a strategic variable. If its strategy is price, the oligopoly is called Bertrand oligopoly with product differentiation, and if it is output, we have Cournot oligopoly with product differentiation. In Bertrand oligopoly with product differentiation, the firm chooses its profit-maximizing price assuming that its rivals’ prices are not affected by its own price choice. On the other

Liquidity and Economic Fluctuations

This paper studies the relationship between liquidity and economic ‡uctuations when …rms endogenously select their leverage level to …nance investment opportunities on which they have private information. The dynamic of leverage decision is the driving force delivering all the main results. First, the analysis provides a theoretically based measure of the liquidity of the economy, i.e. the cross sectional variance in …rm debt yields. Second, it shows why liquidity, investment and the dispersion of leverage levels observed in the bond markets are procyclical. Third, it argues that the theoretical implications of the model are consistent with two novel US …nancial market regularities: (1) the negative correlation between the cross sectional variance in …rm debt yields and the cyclical component of GDP and (2) the positive correlation between cross sectional variance in …rm debt ratings and the cyclical component of GDP. The approach also relates the illiquidity of the economy to the existence of pooling equilibria in the security space. This analysis shows how these kinds of equilibria become surprisingly robust to o¤-equilibrium perturbations.