Predator-prey interactions play important roles in ecological communities. Personality, consistent inter-individual differences in behaviour, of predators, prey or both are known to influence inter-specific interactions. An individual may also behave differently under the same situation and the level of such variability may differ between individuals. Such intra-individual variability (IIV) or predictability may be a trait on which selection can also act. A few studies have revealed the joint effect of personality types of both predators and prey on the dynamics of prey-predator models. In this project we aim to build different mathematical models to study the role of the behavior on prey-predator dynamics. All these models will be fully studied mathematically, and numerical solutions will be given.