Duality structure, asymptotic analysis and emergent fractal sets

  • Dhurjati Prasad Datta University of North Bengal
  • Soma Sarkar

Abstract

A new, extended nonlinear framework of the ordinary real analysis  incorporating a novel concept of {\em duality structure} and its applications into  various nonlinear dynamical problems is presented. The duality structure is an asymptotic property that should affect the late time  asymptotic behaviour of a nonlinear dynamical system in a nontrivial way leading naturally to signatures generic to a complex system. We argue
that the present formalism would offer a natural framework to understand the abundance of complex systems in natural, biological, financial and related problems. We show that the power law attenuation of a dispersive, lossy wave equation, conventionally deduced from fractional calculus techniques, could actually arise from the present asymptotic duality structure. Differentiability on a Cantor type fractal set is also formulated.

Published
Aug 26, 2018
How to Cite
DATTA, Dhurjati Prasad; SARKAR, Soma. Duality structure, asymptotic analysis and emergent fractal sets. Nonlinear Studies, [S.l.], v. 25, n. 3, p. 609-640, aug. 2018. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1683>. Date accessed: 22 sep. 2018.