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The evolution of the conflict of “blackmail” between two individuals is dealt with—both for symmetric and asymmetric contests. State—space diagrams are presented illustrating the dynamical coevolution of the cooperathe propensities of the partners when the games are played inductively—and learning takes place via storing the result of the previous outcome. By changing the three parameters of the game α, č, k (the probability of yield— “chicken”—the tempting factor and the coefficient of mutual loss, respectively) we can modify drastically the probability of “locking‐in” at the cooperative state as well as the dynamical repertoire for each contestant (i.e. the number of states between which his strategy undergoes transitions as well as the probabilities of these transitions). Finally, we study the result of additive white noise on the trajectories of the cooperative propensities, both in the symmetric and the asymmetric case.

The purpose of this paper is to develop a linearized equivalent electrical circuit of a photovoltaic generator. This circuit is appropriate to confront problems such as numerical instability, increased computational time and nonlinear/non‐canonical form of system equations that arise when a photovoltaic system is modelled, either with differential equations or with equivalent resistive circuits that are generated by electromagnetic transient software packages for power systems studies.

The proposed technique is based on nonlinear and well‐tested i_pv−v_pv equations which are however used in an alternative mathematical manner. The application of the Newton‐Raphson algorithm on the i_pv−v_pv equations leads to uncoupling of the i_pv and v_pv quantities in each time step of a digital simulation. This uncoupling is represented by a linearized equivalent electrical circuit.

The application of nodal analysis equivalent resistive circuits using the proposed equivalent photovoltaic generator circuit leads to a system model based on linear algebraic equations. This is in opposition to the nonlinear models that normally result when a nonlinear i_pv−v_pv equation is used. In addition, using the proposed scheme, the regular systematic methods of circuit analysis are fully capable of deriving the differential equations of a photovoltaic system in standard form, thus avoiding the time‐consuming solution process of nonlinear models.

In this paper, a new method of using the i_pv−v_pv characteristic equations is proposed which remarkably simplifies photovoltaic systems modeling. Moreover, a very important practical application is that by using this methodology one can develop a photovoltaic generator element in electromagnetic transient programs for power systems analysis, of great value to power engineers who are involved in photovoltaic systems modeling.

Presents a new approach for formulating the state space equations associated with electrical systems containing circuits which are coupled only magnetically. Presents an algorithm which automatically determines the state space matrix of a system which can take any topological form. Describes a new way of representing semiconductor devices which gives increased flexibility in system representation, and reduces computation time, together with a technique for satisfactorily accounting for the discontinuous behaviour of semiconductor devices. Illustrates the application of the proposed technique by means of a relatively simple example for which an analytical solution is possible. Compares illustrative test results obtained from more complex circuits with those from simulation to demonstrate further the validity of the method.