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Higher dimensional differential equations may express several real world simulation processes which depend upon their pre-history and subject to short-time disturbances. Such processes occur in the theory of optimal control, population dynamics, biotechnologies, economics, mathematical physics etc. So, the study of this class of dynamical systems is gradually gaining momentum. In the present work Avery-Peterson theorem has been envisaged for getting the positive periodic solutions of the corresponding differential equations for cones with impulses on time scales. By using the multiple fixed-point theorems we have shown through different lemmas and manipulation of several functions how the necessary criteria can be mathematically arrived at so that the results come to be feasible as well as effective. Keywords: Real world simulation processes; Theory of optimal control; Population dynamics; Biotechnologies; Economics The Himalayan Physics Vol.2, No.2, May, 2011 Page: 50-53 Uploaded Date : 1 August, 2011

Higher Dimensional Differential Equations for Some Real World S imulation Processes and Solutions Thereof