A numerical exploration of the dynamical behaviour of q-deformed nonlinear maps Vinod Patidar 1 , G. Purohit and K K Sud Department of Basic Sciences, School of Engineering Sir Padampat Singhania University, Bhatewar, Udaipur – 313601, INDIA 1 Email: vinod_r_patidar@yahoo.co.in Abstract: In this paper we explore the dynamical behaviour of the q- deformed versions of widely studied 1D nonlinear map-the Gaussian map and another famous 2D nonlinear map-the Henon map. The Gaussian map is perhaps the only 1D nonlinear map which exhibits the co-existing attractors. In this study we particularly, compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a special attention on the regions of the parameter space, where these maps exhibit co-existing attarctors. We also generalize the q-deformation scheme of 1D nonlinear map to the 2D case and apply it to the widely studied 2D quadratic map-the Henon map which is the simplest nonlinear model exhibiting strange attractor. Keywords: q-deformation, Gaussian map, Henon map, Lyapunov exponent, Chaos, co-existing attractors 1. Introduction The fascinating theory of quantum groups has attracted considerable interest of physicists and mathematicians towards the special branch of mathematics dealing with q-deformed versions of numbers, series, functions, exponentials, differentials etc. (i.e. the q-mathematics) [1]. The q-deformation of any function is to introduce an additional parameter (q) in the definition of function in such a way that under the limit 1  q , the original function is recovered. Hence there exist several deformations of the same function. A recent study [2] induced the study of q-deformation of nonlinear dynamical system, where a scheme for the q-deformation of nonlinear maps (in analogy to the q-deformation of numbers, functions, series etc.) has been suggested. In this study authors have shown that the q-deformed version of logistic map (q-logistic map) exhibits a variety of interesting dynamical behaviours (which also exist in the canonical logistic map) including the co-existing attractors, which are not present in canonical logistic map. Further Patidar [3] and Patidar et al. [4] analyzed the dynamical behaviour of q-deformed version of another famous 1D map – the Gaussian map, which is perhaps the only known 1D map, exhibiting co-existing attractors. In this paper, we present the results of our recent analysis of the dynamical behaviour of various q-deformed maps. Particularly, we report the results of numerical exploration of the dynamical behaviour of q-deformed versions of widely studied 1D nonlinear map-the Gaussian map and another famous 2D nonlinear map-the Henon map.