Jump Equilibria in Public-Good Differential Games with a Single State Variable

2022 ◽  
Author(s):  
Johannes M. Schumacher ◽  
Puduru Viswanadha Reddy ◽  
Jacob C. Engwerda
Keyword(s):  
Public Good ◽  
Differential Games ◽  
State Variable ◽  
Single State

Jump Equilibria in Public-Good Differential Games with a Single State Variable

2021 ◽  
Author(s):  
J.M. (Hans) Schumacher ◽  
Puduru Viswanadha Reddy ◽  
Jacob C. Engwerda
Keyword(s):  
Public Good ◽  
Differential Games ◽  
State Variable ◽  
Single State

scholarly journals The Design and Its Application in Secure Communication and Image Encryption of a New Lorenz-Like System with Varying Parameter

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Lilian Huang ◽  
Donghai Shi ◽  
Jie Gao
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
State Feedback ◽  
Complex Dynamic ◽  
State Variable ◽  
Encryption And Decryption ◽  
Single State ◽  
Chaotic Parameter ◽  
Synchronization Scheme ◽  
New System

A new Lorenz-like chaotic system with varying parameter is proposed by adding a state feedback function. The structure of the new designed system is simple and has more complex dynamic behaviors. The chaos behavior of the new system is studied by theoretical analysis and numerical simulation. And the bifurcation diagram shows a chaos-cycle-chaos evolution when the new parameter changes. Then a new synchronization scheme by a single state variable drive is given based on the new system and a chaotic parameter modulation digital secure communication system is also constructed. The results of simulation demonstrate that the new proposed system could be well applied in secure communication. Otherwise, based on the new system, the encryption and decryption of image could be achieved also.

scholarly journals A homogenization result for interacting elastic and brittle media

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180118 ◽  
Author(s):  
Andrea Braides ◽  
Andrea Causin ◽  
Margherita Solci
Keyword(s):  
Skeletal Muscles ◽  
Gamma Convergence ◽  
High Contrast ◽  
Contrast Effects ◽  
Convex Functional ◽  
State Variable ◽  
Reference Set ◽  
Hybrid Laminates ◽  
Interaction Term ◽  
Single State

We consider energies modelling the interaction of two media parameterized by the same reference set, such as those used to study interactions of a thin film with a stiff substrate, hybrid laminates or skeletal muscles. Analytically, these energies consist of a (possibly non-convex) functional of hyperelastic type and a second functional of the same type such as those used in variational theories of brittle fracture, paired by an interaction term governing the strength of the interaction depending on a small parameter. The overall behaviour is described by letting this parameter tend to zero and exhibiting a limit effective energy using the terminology of Gamma-convergence. Such energy depends on a single state variable and is of hyperelastic type. The form of its energy function highlights an optimization between microfracture and microscopic oscillations of the strain, mixing homogenization and high-contrast effects.

Targeting Temporal Patterns in Time-Delay Chaotic Systems

2014 ◽  
Vol 24 (02) ◽  
pp. 1450014 ◽  
Author(s):  
Sourav K. Bhowmick ◽  
Dibakar Ghosh ◽  
Pousali Roy ◽  
Syamal K. Dana ◽  
K. Murali ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Temporal Patterns ◽  
Threshold Value ◽  
Threshold Level ◽  
Control Of Chaos ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
State Variable ◽  
Potential Applications ◽  
Single State

We report a control of chaos in time-delayed nonlinear systems, which constitute an important class of infinite-dimensional systems. Our method simply entails clipping of a single state variable of the chaotic system to a threshold value. The method is easier to implement since only a single variable is needed to be accessible for measurement and resetting. A variation of the threshold level yields a wide variety of regular temporal patterns. The important advantage of this method is that it generates a look-up table, which can be readily used to obtain a desired behavior by just setting the corresponding threshold value. Such a feature makes this control of chaotic systems attractive for potential applications. We physically verify the technique in an electronic experiment.

scholarly journals Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns

Economies ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 77
Author(s):  
George E. Halkos ◽  
George J. Papageorgiou
Keyword(s):  
Differential Games ◽  
Stackelberg Game ◽  
Pollution Abatement ◽  
Control Policy ◽  
Open Loop ◽  
Social Planner ◽  
Nash Game ◽  
State Variable ◽  
Polluting Firms ◽  
Analytical Expressions

In this paper we model the conflict between the group of polluting firms in a country and any social planner in the same country who attempts to control the volume of emissions generated during the production process. Both players of the game have their own control policies, i.e., the rate of emissions on behalf of the polluting firms and the rate of pollution control (e.g., pollution abatement or environmental taxation) on behalf of the home country. The common state variable of the model is the number of polluting firms, which aims to be minimized via the country’s control policy, but on the polluters’ side it is beneficial to be maximized. Regarding the game model, its setup belongs to the special class of differential games, which are called ‘state separable differential games’. An important property of these games is that the open-loop Nash equilibrium coincides with the Markovian (closed-loop) equilibrium and, in the case of hierarchical moves, analytical solutions are easily obtained. The game proposed here is analyzed for both types of equilibrium, i.e., Nash and Stackelberg. In the simultaneous move game (i.e., the Nash game) we find the equilibrium’s analytical expressions of the controls for both players, as well as the stationary value of the stock of polluting firms. A sensitivity analysis of the model’s crucial variables takes place. In the hierarchical move game (i.e., the Stackelberg game) we find the equilibrium values of the controls, as well as of the state variable. As a result, a comparison between the two types of equilibrium for the game takes place. The analysis of the comparison reveals that the conflict is more intensive (since both controls have greater values) for the case in which the polluting firms act as the leader in the hierarchical move game.

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