Mathematical model on influence of past experiences on present activities of human brain

Abstract

This article explores how emotional feelings linked to stored memories of past experiences influence the present activity of the human brain. To analyse this, a mathematical model is considered describing the dynamics in a two-layered network in which the neurons in the first layer are involved in present activities and are influenced by cells in the second layer that carry the emotional feelings associated with memories of past experiences. Initially, this article establishes sufficient conditions for the stability of a unique equilibrium solution in the system for both constant and time-varying exogenous inputs. This indicates the situation where the present activities are not disturbed by emotions emanated from past memories. Furthermore, it is observed that certain variations in the exogenous inputs can induce oscillations within the system. To manage them, this study suggests the adjustment of specific parameters that could actually control certain fluctuations according to emotional responses to past and current memories. This control aims to stabilize the brain’s current activity, allowing it to reach a balanced state.

Keywords

• neural networks
• time delays
• equilibria
• global stability
• emotions
• memory
• 34d23
• 34k20
• 92b20
• 93d20