In this paper it is shown a mathematical analysis that tries to improve the modelling of Case based reasoning system (CBR). It is well known that uncertain environments are one of the main difficulties to obtain successful performance when CBR models are used. In general, when an adaptive intelligent system has to deal in highly dynamic environments, and “wants to survive”, it needs an efficient equilibrium between high-level processes (deliberative and time-costly) and low-level ones (reactive, faster but poorer in quality). It is simply one of the shapes of the classical exploration/exploitation dilemma that characterizes the behaviour of technological devices in many fields. Recent research has shown that there is neither an optimal nor a unique solution for this problem. In this paper, we have developed an approach based on dynamical systems that propose a standard mechanism to calculate the optimum point regardless of how the problem is represented.