Pursuit Evasion Game (PEG) is an abstract model of various significant problems that appear in both civil and military applications. Bio-Inspired strategies are found to be very useful in studying the PEG. While optimal response to the pursuit strategies are available using geometric control theory, it is shown in this paper that application of linear feedback control laws can further improve the time and tracking response of these strategies in capturing the evader by the pursuer. Empirical results based on computer simulation are used to illustrate the findings. Further, considering the case of sudden turn of the evader, moving at a lower speed, it is shown that both in theory and simulation that the evader can delay the capture by pursuer and in some cases even escape from being captured. These findings are in line with what is found in nature.