A cooperative game theoretic model of dynamics of the trust level between subjects of the system of optional professional education is proposed. Some approaches to the model identification and investigation based on simulation modeling and differential cooperative game theory are considered.

Keywords: social partnership, optional professional education, differential cooperative games, simulation modeling, identification

Relations between subjects of the system of social partnership in the domain of optional professional education are modeled by a voting game. For the 3-person voting game a comparative analysis of such optimality principles as C-core, NM-decision, and Shapley value for the typical values of the players' voices is conducted.

Keywords: social partnership, optional professional education, voting games, C-core, NM-decision, Shapley value

  This article presents an agent-based computational model of civil violence. In the model a central authority seeks to suppress communal violence between two warring ethnic groups. To describe model UML diagrams are presented. Article also shows a number of experiments with model which shows such benefits of model as guiding data collection, revealing dynamical analogies, discovering new questions and decision support in crisis situations.

Keywords: Legitimacy, agent based modeling, simulation, risk aversion, jail, neighborhood patches, radius vision, expressed political tension, latent political tension

The paper reports on dynamical model of optimal biological resource exploitation with corruption. Particularly, it is allowed a fish quota increase after paid a bribe. The research has been realized with the sustainable development conception by the Pontryagin's maximum principle. A time moment, where the bribe is profitable, is considered. Fight corruption methods are presented.

Keywords: Mathematical model, optimal exploitation, corruption

  The article is devoted to the problem of the research of geopolitical processes on the world regions’ scale under present-day conditions. The article substantiates the necessity of their analysis with the help of the cognitive approach as an effective means of cognition of the interconnections and interrelationships within the complicated systems. With that aim in view the specifics and the stages of the cognitive modeling are given thorough analysis in the article. This type of modeling is adapted to the analysis of geopolitical dynamics on the regional/sub regional level taking into consideration its aptitudes to make prognostic scenarios of the development of the situation. The possibilities of the cognitive modeling of geopolitical processes are illustrated on the example of the situation in three sub regions constituting one (big) the Black Sea – Caspian region.

Keywords: World regions, geopolitical processes, modeling of the complicated systems, modeling of the geopolitical processes, cognitive modeling, the program’s system of the cognitive modeling, the Black Sea – Caspian Region, the Black Sea sub region, the Caucasus

In the article the analysis of conflictogenic potential of the North Caucasus as one of the most troubled regions of modern Russia is presented. It is shown that the inertial scenario of its development realized in modern Russia with relief local specifics is distinctly noticeable in social dynamics of the North Caucasus as well.

Keywords: conflictogenic potential, development scenario, social dynamics, troubled region, the North Caucasus.

This article presents an agent-based computational model of civil violence. In the model we present variant of civil violence when central authority seeks to suppress decentralized rebellion. This model involves two categories of actors. ‘‘Agents’’ are members of the general population and may be actively rebellious or not. ‘‘Cops’’ are the forces of the central authority, who seek out and arrest actively rebellious agents. Both type of actors are having attributes and behavioral rules.

Keywords: Legitimacy, Grievance, Perceived Hardship, Risk Aversion, Jail, Neighborhood, Vision Radius, Salami Tacktics, Initial Density, Active Agent, Quiet Agent, Civil Violence, Visualization, Tension, Ripness Index.

The mathematical model formalizes the solution of a problem of optimum control and it is meaningful to minimization of number of regional extremist system (bandit underground) taking into account relative importance of parts making it at the restrictions caused by "will" of the state to fight against extremism and objective dynamics of number of groups of extremists, an ethnosociocultural protestnost defined by factors (protest potential of society). The task was solved by means of imitating modeling on a method of scenarios.

Keywords: Mathematical model, method of scenarios, extremism, dynamics of number of groups of extremists, problem region, North Caucasus.

It is shown that for research of difficult processes of social interaction at the present stage of development of system modeling hierarchical systems of cognitive models, cognitive architecture and the integrated systems of modeling are even more often used. With reference to these processes the system of models should reflect various abstractions of the description of structure, various aspects of her behavior, stages (iterations) of its evolution in the course of functioning and development. It is offered to consider architecture of set of models in a need context for the solution of a task at a concrete investigation phase.

Keywords: process of social interaction, research, modeling, modeling technologies, systems modeling.

The mathematical model formalizes the solution of a problem of optimum control and  the minimization of regional extremist system’s number (bandit underground) is meaningful taking into account the relative importance of its parts with the restrictions caused by "will" of the state to fight against extremism and the objective dynamics of the extremist groups number, defined by the ethno-and-sociocultural protest potential factors. The problem was solved by means of imitating modeling basing on scenarios method. The results of scenery modeling of republican bandit underground dynamics are obtained depending on different variants of the power influence, in conjunction with different options of republican community development. The results of modeling calculations on fixing of a range of scenarios of quantitative dynamics of separate groups layers of a republican bandit underground are given. The identification of modeling parameters according to scenarios is executed and interpretation of the received results and practical recommendations on optimization of combating regional terrorist underground is presented.

Keywords: Mathematical model, scenery modeling, extremism, bandit underground, dynamics of number of groups layers of extremists, problem region, North Caucasus.