scientists are interested in find out “how to use living resources without damaging the ecosystem at the same time?” from nineteen century because the living resources are limited. thus, the harvested rate is used as the control parameters. moreover, the study of harvested population dynamics is more realistic.    in the present paper, some predator-prey models in which two ecologically interac...

We characterize belief-free equilibria in infinitely repeated games with incomplete information with an arbitrary number of players and arbitrary information structures. This generalizes Hörner and Lovo (2008), which restrict attention to the two-player case and to information structures that have a product structure. Our characterization requires introducing a new type of individual rational c...

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N ≥ 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; ...

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N ≥ 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; ...

In this article, a new fractional order one–country game model (OCGM) with distinct incidence is explored. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The basic reproduction numbers R0 = β (α+1)(γ+μ) and R∗ 0 = E rv are found. It is shown that the...

in this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{ax_n+x_{n-1}}{b+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $a, b$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

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The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature, in out-of-equilibrium conditions at which the interfacial free energy is ill-defined. Here we draw a connection between the atomistic description of a diffus...

Manipulators with free joints are second-order nonholonomic systems whose dynamical constraints are nonintegrable. Such systems are known to be underactuated systems which can be controlled by less actuator than the dimension of the configuration space. Previously proposed methods to control free-joint manipulators have been based on the assumption of perfectly frictionless free joints. In this...