International Journal of Pure and Applied Mathematics Volume 104 No. 4 2015, 509-516 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v104i4.2 P A ijpam.eu STABILITY AND LYAPUNOV EXPONENTS OF A q-DEFORMED MAP Bhagwati Prasad 1 § , Kuldip Katiyar 2 1,2 Department of Mathematics Jaypee Institute of Information Technology A-10, Sector-62, Noida, UP-201307 INDIA Abstract: The aim of this paper is to study the stability analysis of q- deformed chaotic map under Mann iterative scheme. We also plot the time series and Lyapunov exponent for changing values of the parameters. AMS Subject Classification: 37B25, 37C75, 65P40 Key Words: logistic map, q-deformation, Mann iteration, Lyapunov expo- nent 1. Introduction Verhulst postulated that the growth rate at any time should be proportional to the fraction of the environment that is not yet used up by the population at that time. The discrete version of the Verhlusts model was further expressed by R. May [12] by the following difference equation x n+1 = rx n (1 − x n ), (1) where x n (a real number between 0 and 1) represents population density at time n =1, 2, 3, ... and r is used for the combined rate for reproduction and starvation (see also [13] and [15]). Received: April 17, 2015 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author