Multiple Stable Equilibria in an Optimizing Perfect-Foresight Model

Econometrica ◽  
1984 ◽  
Vol 52 (1) ◽  
pp. 223 ◽  
Author(s):  
Maurice Obstfeld
Keyword(s):  
Perfect Foresight ◽  
Stable Equilibria ◽  
Multiple Stable Equilibria

scholarly journals Design and Optimal Control of a Multistable, Cooperative Microactuator

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 183
Author(s):  
Michael Olbrich ◽  
Arwed Schütz ◽  
Tamara Bechtold ◽  
Christoph Ament
Keyword(s):  
Deflection Angle ◽  
Initial State ◽  
New Concepts ◽  
Vertical Displacements ◽  
State Uncertainty ◽  
Stable Equilibria ◽  
Freely Moving ◽  
Time And Energy ◽  
Multiple Stable Equilibria ◽  
Optimal Trajectory Planning

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty.

Dynamic Response of Dielectric Elastomers

2004 ◽  
Author(s):  
Eric M. Mockensturm ◽  
Nakhiah Goulbourne
Keyword(s):  
Large Deformations ◽  
Electrical Energy ◽  
Material Behavior ◽  
Dielectric Elastomers ◽  
Large Strains ◽  
Inertial Effects ◽  
Stable Equilibria ◽  
Electrostatic Pressure ◽  
Linear Material ◽  
Multiple Stable Equilibria

Dielectric elastomers have received a great deal of attention recently for effectively transforming electrical energy to mechanical work. Their large strains and conformability make them enticing materials for many new types of actuators. Unfortunately, their non-linear material behavior and large deformations make actual devices difficult to model. However, the reason for this difficulty can also be used to design actuators that utilize these material and geometric non-linearities to obtain multiple stable equilibria. In this work, we investigate one of the simplest possible configurations, a spherical membrane, using a model that incorporates both mechanical and electrostatic pressure as well as inertial effects that become important when transitioning from one equilibrium to another.

Chaebol and Catastrophe: A New View of the Korean Business Groups and Their Role in the Financial Crisis

2002 ◽  
Vol 1 (2) ◽  
pp. 1-45 ◽  
Author(s):  
Robert C. Feenstra ◽  
Gary G. Hamilton ◽  
Eun Mie Lim
Keyword(s):  
Industrial Organization ◽  
Business Groups ◽  
High Concentration ◽  
Low Concentration ◽  
Korean Economy ◽  
Vertical Linkages ◽  
Stable Equilibria ◽  
Second Tier ◽  
The Government ◽  
Multiple Stable Equilibria

We present a model of industrial organization that has multiple stable equilibria and argue that the high-concentration equilibrium describes Korea's economy and the low-concentration equilibrium describes Taiwan's economy. Past industrial policy of the state may have put Korea's economy in the high-concentration equilibrium, but discontinuation of the policy did not cause the industrial organization to change because this is an economically viable equilibrium. The high-concentration equilibrium produces a narrower range of final goods than the low-concentration equilibrium, which explains why the 1996 collapse in semiconductor prices caused the less diversified Korean economy to contract more than the more diversified Taiwanese economy. More importantly, this collapse in demand caused Korea's economy to move to a new equilibrium that has a smaller number of business groups, as evidenced by the collapse of the second-tier chaebol and their absorption into the first-tier chaebol. This wave of bankruptcies, combined with the financially precarious state of the merchant banks, created an investor panic that precipitated the crisis, which began with the 17 November 1997 devaluation of the won. This is why economic fundamentals could explain the chaebol bankruptcies before that date and not those after that date. The logic of our model suggests that public policy should focus on reducing the vertical linkages within business groups and not on reducing their horizontal linkages as the current “Big Deal” program of the government is doing.

scholarly journals Pleiotropy as a factor maintaining genetic variation in quantitative characters under stabilizing selection

1996 ◽  
Vol 68 (1) ◽  
pp. 65-73 ◽  
Author(s):  
A. Gimelfarb
Keyword(s):  
Allelic Frequency ◽  
Direct Selection ◽  
Stabilizing Selection ◽  
Major Locus ◽  
Relative Contribution ◽  
Linkage Disequilibria ◽  
Wide Range ◽  
Stable Equilibria ◽  
A Minor ◽  
Multiple Stable Equilibria

SummaryA model of pleiotropy with N diallelic loci contributing additively to N quantitative traits and stabilizing selection acting on each of the traits is considered. Every locus has a major contribution to one trait and a minor contribution to the rest of them, while every trait is controlled by one major locus and N−1 minor loci. It is demonstrated that a stable equilibrium with the allelic frequency equal to 0·5 in all N loci can be maintained in such a model for a wide range of parameters. Such a ‘totally polymorphic’ equilibrium is maintained for practically any strength of selection and any recombination, if the relative contribution by a minor locus to a trait is less than 20 % of the contribution by a major locus. The dynamic behaviour of the model is shown to be quite complex with a possibility under sufficiently strong selection of multiple stable equilibria and positive linkage disequilibria between loci. It is also suggested that pleiotropy among loci controlling traits experiencing direct selection can be responsible for apparent selection on neutral traits also controlled by these loci.

scholarly journals A NUMERICAL SIMULATION OF THE ONE-LOCUS, MULTIPLE-ALLELE FERTILITY MODEL

Genetics ◽  
1986 ◽  
Vol 113 (1) ◽  
pp. 161-176
Author(s):  
Andrew G Clark ◽  
Marcus W Feldman
Keyword(s):  
Numerical Simulation ◽  
Multiple Allele ◽  
Viability Selection ◽  
Equilibrium Behavior ◽  
Mean Fitness ◽  
Stable Equilibria ◽  
The Mean ◽  
The One ◽  
Multiple Stable Equilibria ◽  
Stable Points

ABSTRACT Numerical simulations were performed to determine the equilibrium behavior of the one-locus fertility model in which fitness is considered as a property of a pair of mating diploids. A series of patterns of "fertility matrices" were considered for a single locus with two to six alleles. From these simulations, 19 different statistics were collected that characterize, at equilibrium, the heterozygosity, the mean fitness and the fate of populations begun at the allele-frequency centroid. For more than one-half of the trajectories produced by random fertility matrices, there was a decrease in the mean fitness at some time on the way to equilibrium. The mean number of alleles maintained at equilibrium increased only slightly with matrix dimension. Despite the potential for fertility models to display multiple stable equilibria, random fertility models maintain fewer distinct stable points than do random one-locus viability models. Pleiotropic models were also considered with fertility and viability selection operating sequentially within each generation. Most of the equilibrium statistics (with the exception of mean fertility) for the pleiotropic model were intermediate between the corresponding random viability and fertility models.

A Note on Trial Delay and Social Welfare: The Impact of Multiple Equilibria

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Tim Friehe ◽  
Thomas J. Miceli
Keyword(s):  
Social Welfare ◽  
Multiple Equilibria ◽  
Policy Implications ◽  
Important Policy ◽  
Deterrence Effect ◽  
Stable Equilibria ◽  
The Impact ◽  
Multiple Stable Equilibria

AbstractGreater trial delay is commonly associated with decreasing demand for trials, thereby bringing about an equilibrium for a given trial capacity. This note highlights that – in contrast to this premise – trial delay may in fact increase trial demand. Such an outcome is established for a scenario in which the number of cases is endogenous based on the deterrence effect of lawsuits. That trial demand may increase with longer delay makes multiple stable equilibria possible. This reality has important policy implications, which are discussed.

scholarly journals Subthreshold domain of bistable equilibria for a model of HIV epidemiology

2003 ◽  
Vol 2003 (58) ◽  
pp. 3679-3698 ◽  
Author(s):  
B. D. Corbett ◽  
S. M. Moghadas ◽  
A. B. Gumel
Keyword(s):  
Hiv Transmission ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Stability Analysis ◽  
Hiv Epidemiology ◽  
Preventive Vaccine ◽  
Hiv Eradication ◽  
Stable Equilibria ◽  
Multiple Stable Equilibria ◽  
Anti Hiv

A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (ℛ0) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible ifℛ0<ℛ∗, whereℛ∗is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs whenℛ∗<ℛ0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

scholarly journals The dynamics of cooperation, power, and inequality in a group-structured society

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Denis Tverskoi ◽  
Athmanathan Senthilnathan ◽  
Sergey Gavrilets
Keyword(s):  
Social Dynamics ◽  
Collective Actions ◽  
Agent Based ◽  
Political Inequality ◽  
Equilibrium Dynamics ◽  
Analytical Approximations ◽  
Group Cooperation ◽  
Stable Equilibria ◽  
Large Groups ◽  
Multiple Stable Equilibria

AbstractMost human societies are characterized by the presence of different identity groups which cooperate but also compete for resources and power. To deepen our understanding of the underlying social dynamics, we model a society subdivided into groups with constant sizes and dynamically changing powers. Both individuals within groups and groups themselves participate in collective actions. The groups are also engaged in political contests over power which determines how jointly produced resources are divided. Using analytical approximations and agent-based simulations, we show that the model exhibits rich behavior characterized by multiple stable equilibria and, under some conditions, non-equilibrium dynamics. We demonstrate that societies in which individuals act independently are more stable than those in which actions of individuals are completely synchronized. We show that mechanisms preventing politically powerful groups from bending the rules of competition in their favor play a key role in promoting between-group cooperation and reducing inequality between groups. We also show that small groups can be more successful in competition than large groups if the jointly-produced goods are rivalrous and the potential benefit of cooperation is relatively small. Otherwise large groups dominate. Overall our model contributes towards a better understanding of the causes of variation between societies in terms of the economic and political inequality within them.

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