### ANALYSIS OF THE GROWTH RATE OF FEMININE MOSQUITO THROUGH DIFFERENCE EQUATIONS

Regan Murugesan     (Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, # 42 Avadi-Vel Tech Road, Avadi, Chennai- 600062, Tamil Nadu, India)
Sathish Kumar Kumaravel     (Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, # 42 Avadi-Vel Tech Road, Avadi, Chennai- 600062, Tamil Nad, India)
Suresh Rasappan     (Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences- Ibri, PO Box 466, Postal Code 516, Ibri, Sultanate of Oman, Oman)
Wardah Abdullah Al Majrafi     (Mathematics Section,Department of Information Technology, College of Computing and Information Sciences University of Technology and Applied Sciences- Ibri, PO Box 466, Postal Code 516, Ibri, Sultanate of Oman, Oman)

#### Abstract

The mosquito life cycle is developed mathematically with the concept of difference equation. The qualitative properties of the life-cycle are analyzed. The Lyapunov function is defined for difference equation to stabilize the system of mosquito life cycle. A novel technique is applied for deriving stability criterion, especially the back-stepping control technique is applied for discrete time system. The bifurcation analysis is also furnished for the model of mosquito life cycle. The new technique is applied in the mosquito life cycle model and its results are examined through MATLAB.

#### Keywords

Difference Equation, Mosquito, Bifurcation, Equilibrium, Strict Feedback

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