Cognitive ageing seems to be a story of global degradation. As one ages there are a number of physical, chemical and biological changes that take place. Therefore it is logical to assume that the brain is no exception to this phenomenon. The principle purpose of this project is to use models of neural dynamics and learning based on the underlying principle of self-organised criticality, to account for the age related cognitive effects. In this regard learning in neural networks can serve as a model for the acquisition of skills and knowledge in early development stages i.e. the ageing process and criticality in the network serves as the optimum state of cognitive abilities. Possible candidate mechanisms for ageing in a neural network are loss of connectivity and neurons, increase in the level of noise, reduction in white matter or more interestingly longer learning history and the competition among several optimization objectives. In this paper we are primarily interested in the affect of the longer learning history on memory and thus the optimality in the brain. Hence it is hypothesized that prolonged learning in the form of associative memory patterns can destroy the state of criticality in the network. We base our model on Tsodyks and Markrams [49] model of dynamic synapses, in the process to explore the effect of combining standard Hebbian learning with the phenomenon of Self-organised criticality. The project mainly consists of evaluations and simulations of networks of integrate and fire-neurons that have been subjected to various combinations of neural-level ageing effects, with the aim of establishing the primary hypothesis and understanding the decline of cognitive abilities due to ageing, using one of its important characteristics, a longer learning history.