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The spread of epidemics over a landscape of several population agglomerations is presented. A continuous, system dynamics version of an epidemics model is discussed and compared to the agent-based model. The validity of the continuous Susceptible-Infected-Recovered-Susceptible (SIRS) model is questioned. The main model deficiencies are the lack of the influence of the collective memory of the population and the spatial distribution of individuals. The chaotic behavior of the agent-based model is pointed out as a better approximation of the true dynamics of an epidemic.
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The problem being investigated is the spontaneous rise of the herd instinct in an artificial population, where the population members have no explicit stimuli for such instinct implanted in their original behavior patterns. The simulations are focused on the creation of the herd instinct in the population that originally does not reveal the gregarious behavior. In this agent-based model, the members of the population (agents) move over a limited region, look for renewable food, reproduce, escape a threat and die. The evolution of the herd instinct is simulated. No explicit instinct is imposed on the agents. It is pointed out that both the search for food and fear, are factors that cause the rise of the herd instinct. The evolution of the amount of the instinct is slow and needs long model time intervals, running over several hundred generations of the agents. The herd instinct is inherited from parent agents during the reproduction, with certain random deviation. This makes the total amount of the instinct evolve and reach an optimal level.
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The article is focused on applications of the differential inclusions to the models of economic growth, rather than the model building. The models are taken from the known literature, and some modifications are introduced to reflect an additional inertia. The aim is to treat the uncertainty in the model parameters by using differential inclusions instead of the stochastic approach. The reachable sets for the models are shown, to assess the possible ranges of the outcome with given parameters uncertainty. The approach may be interpreted as a generalization to the system dynamics methodology, providing attainable sets instead of single model trajectory and simple sensitivity analysis. A comparison with Powersim risk analysis is provided. The models of Solow and Swan, Mankiw, Bhattacharya, Romer and Weil are used. A brief review of the models is given, and several examples of simple simulations, differential inclusion applications and optimization are presented.
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The prey-predator model in the form of Lotka-Volterra equation represents a nonlinear description of the dynamics of two or more interacting populations. In this article, several versions of the Lotka-Volterra model are analyzed from the point of view of parameter uncertainty. The uncertainty treatment is quite different from the common approach. We do not treat uncertain parameters as random. Instead, we analyze the behavior of the models supposing that the uncertain parameters may change in time within given limits. The simulation tool used in this paper is based on the differential inclusions, instead of the ordinary differential equations. This permits us to determine the attainable sets in the state space, due to the parameter uncertainty.
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A model of the dynamics and interactions between organizations with self-organizing hierarchical structures is presented for discrete events. The active objects of the model are individuals (people, organization members). The parameters of an individual are ability, corruption level, resources, and lust for power, among others. Three organizations are generated and interact with each other, attempting to gain more members and power. The individuals appear and disappear, due to a simple 'birth-and-death' process. If an individual disappears from the model, a corresponding reconfiguration in the hierarchical structure occurs. The organization's growth and macro-patterns are the result of the activities of the individuals. The aim of the simulation is to visualize the evolution of the organizations and the stability of the whole system. A 'steady state' for the model is rare; instead, in most parameter configurations, the model enters into oscillations.
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A simple model of a self-destructing society is presented. It can be interpreted as a game with two players: the society and its sub-set which tends to destroy the whole society, as well as itself. The main factor taken into account in the model is the progress of science and technology which provides the destruction tools (new weapons and killing techniques), as well as tools the society can use to defend itself. The modeling and simulation tool is discrete-event and can be treated as agent-oriented, though the agent capabilities are rather simple. The simulation experiments show that, in the near future, this progress will become extremely dangerous, and it may result in the total destruction of mankind. For the longer time period, however, the conclusion is not so pessimistic. If the society survives during a certain time interval, then the probability of survival becomes greater for a longer time span.