JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: VoL 74, No. 2, AUGUST 1992 On the Controllability of Predator-Prey Systems' M. C. JOSHI2 AND R. K. GEORGE 3 Communicated by M. Pachter Abstract. In this paper, we obtain both global and local controllability results for a general nonautonomous predator-prey system using some techniques of nonlinear functional analysis such as the Schauder fixed- point theorem and contraction mapping principle. Key Words. Controllability, predator-prey systems, dynamical sys- tems, fixed-point theorems, contraction mapping principle, functional analysis. 1. Introduction The analysis of the dynamics of predator-prey equations is of consider- able interest and importance to many fields such as ecology, immunology, etc. There are many models available in the literature for predator-prey systems, and their stability properties have been studied by many authors (see Ref. 1). In this paper, we take a general nonautonomous predator-prey model and investigate the controllability (both global and local) using some techniques of nonlinear analysis. The known standard models such as the Lotka-Volterra model (Ref. 2), the Samuelson model (Ref. 3), and the Freedman and Waltman model (Ref. 4), etc., follow as particular cases of our model. In Section 2, we formulate the model for the dynamics of the predator- prey system. Although the model under investigation is two-dimensional, it can be extended to n-dimensional predator-prey systems. In Sections 3 and 4, we prove the controllability of an n-dimensional abstract nonlinear control system, which contains our predator-prey system as a particular ~The first author would like to thank the Department of Science and Technology of India for sponsoring part of this work through Grant No. DST 12(21)/84-STP II. 2professor, Department of Mathematics, Indian Institute of Technology,Powai, Bombay,India. 3Research StudenL Department of Mathematics, Indian Institute of Technology, Powai, Bombay, India. 243 0022-3239/92/0800-0243506.50/0 © 1992 Plenum Publishing Corporation