Delay Induced Oscillation in a Biochemical Model and Its Control

Abstract

Time delay is one of the common phenomena often observed in chemical and biological processes which induce instability in biochemical reactions. Since stability of a system is an essential requirement for easy ongoing of any process, an effort has been made in this study to determine the stability criteria for time delayed enzymatic reactions. Enzymes play a vital role in several manufacturing areas including drugs, chemicals, polymers, oils, leather etc. These reactions are usually accompanied by some time delay during formation of the products. This arises mainly due to some conformational changes wherein some time is consumed in changing from one intermediate stage to the other. So, delay induced enzymatic reactions imposes an unstable environment which subsequently affects the product formation but such a situation can be effectively controlled by introducing some control parameters to minimize the delay effect. In this research article, a delay induced mathematical model of enzyme kinetic reaction has been developed and the dynamics of the reaction is significantly analyzed. The effect of time delay on the the system has been analyzed both analytically and numerically. Delay induced oscillations of the system is overcome by applying control on the system. Numerical simulation is carried out to explain the analytical outcomes.