International Journal of Knowledge Engineering ISSN: 0976-5816 & E-ISSN: 0976-5824, Volume 3, Issue 1, 2012, pp.-91-94. Available online at http://www.bioinfo.in/contents.php?id=40 A THEORETICAL STUDY OF BIOLOGICAL LOTKA-VOLTERRA ECOLOGICAL MODEL USING COMPREHENSIVE THERMODYNAMIC THEORY OF STABILITY OF IRREVERSIBLE PROCESSES (CTTSIP) RAWAT S.G.1, BHALEKAR A.A.2 AND TANGDE V.M.3* 1Department of Applied Chemistry, Priyadarshini College of Engineering, Nagpur, MS, India. 2Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur, MS, India. 3Department of Applied Chemistry, Smt. Bhagwati Chaturvedi College of Engineering, Nagpur, MS, India. *Corresponding Author: Email-
[email protected] Received: February 28, 2012; Accepted: March 06, 2012 Abstract- The dynamical relationship between predator and prey (Lotka-Volterra model or host-parasitoid system)[1] is one of the dominant themes in ecology. It was observed from the population data that interaction between a pair of predator-prey influences the population growth of both the species. This paper presents the study of thermodynamic stability of periodic Lotka-Volterra system against Prey popula- tion perturbation. The thermodynamic stability of representative model of Lotka-Volterra ecosystem has been investigated using proposed thermodynamic Lyapunov function in CTTSIP [2, 3, 4, 5] which follows the steps of Lyapunov's second method (also termed as direct meth- od) of stability of motion[6, 7]. The thermodynamic Lyapunov function, used herein is the excess rate of entropy production in thermodynam- ic perturbation space that conforms well with the dictates of second law of thermodynamics[8, 9]. Moreover, present study reveals the re- gions of stability, asymptotic stability and instability.