Stability, Chaos And Limit Cycles In Recurrent Cognitive Reasoning Systems

Cognitive reasoning involves human short term memory to update the contextual information about a phenomenon. Recurrent models are often used to represent the dynamics of short term memory. These models often suffer from chaos and limit cycles. This chapter aims at designing a new approach to analyze the dynamical behavior of a cognitive reasoning system. The chapter addresses three distinct recurrent models for cognitive reasoning. The first model refers to a recurrent dynamics of a propositional temporal reasoning system. The principle of analysis to determine stable points for this model is illustrated. The second model represents a specialized cognitive map with an encoding model for weight adaptation, and a recall model for deriving new inferences. The last model considers a cognitive structure of an emotional system, the dynamics of which may suffer from limit cycles and chaos for certain parametric conditions. A method of stabilization of the system is given for the generation of stable inferences.