The research goal is to mount a concerted effort to facilitate the introduction of scaling concepts into amenable topics in system theory in general and biological signals and systems in particular. The research is an extension of the fractal systems concept which originated in our efforts to model the dynamics of the polarized metal-solution interfaces using methods of system theory enhanced by notions of scaling. The research will explore resonant systems with complex singularities arranged in scaling patterns in the s-plane and uncover their link to continuous but non-differentiable functions of the Weierstrass kind. The rich dynamics displayed by such systems demand further theoretical elaboration and simulations. A natural extension is the study the non-minimum phase and non- positive real systems with an eye for modelling l/F-type noises ubiquitous in physiological systems. Recent evidence concerning the genesis of such noises by certain categories of chaotic difference equations will be explored. The design of the new-generation data acquisition, manipulation, and processing schemes aimed at general classes of scaling systems and signals is long overdue. The objective will be to adapt, whenever feasible, existing methods of digital signal processing such that scaling data over broad dynamic ranges can be analyzed effectively and economically. Multifractal theories have been promoted in recent years to account for structural heterogeneities in complex scaling objects. The research will attempt to validate the suitability of multifractals in non-destructive evaluation of biological tissue.
