Dynamical inferences of multifaceted systems

Abstract

Main objective of this thesis work is to study the DYNAMICAL newlineINFERENCES OF MULTIFACETED SYSTEMS . newlineThe Problem discussed in the thesis is as follows: newline To develop mathematical prototypes for systems that require methods newlineand procedures to model the unprecedented complexities in diverse processes newlinespanning a wide range of spatial and temporal scales. The strategies that newlineintegrate multiple layers into the mathematical elements of the intricate systems newlineneeded to solve and reach towards important conclusions. Thus, appropriate newlineformulation of each and every layer of the complex system alongwith newlineconsiderable restrictions are key towards modelling multifaceted systems. newlineA system with nonlinearities most commonly has outputs in no proportion to newlinethe inputs if not analyzed through apt methods. It can be easily observed that for newlinecomplex nonlinear system outputs can never be a weighted sum of independent newlinevariables. This is because relation between outputs and inputs are a many to many newlinemappings. This employs effects of nonlinearities in a system impossible to predict newlineconsidering the randomness. It studies the variation i.e., complexities of a system with newlinethe help of either a set of ODEs nonlinear in nature or nonlinear difference equations newlineor the data corpus. Nonlinearities majorly explore the complexities of evolution in a newlinephenomenon which may otherwise remain unresolved or unnoticed. newlineMathematical models denote the mathematical aspects through formalized newlinemathematical expressions i.e., language. Main advantage is that they analyse any form newlineof phenomenon with the help of theories, philosophies and algorithms. As discussed, newlinethese models have been in use from long time and have aided to formulate umpteen newlineproblems mathematically for various purposes. Multifaceted systems focus on the newlineapplicability of the models that are most appropriate for the real-life situation. This newlinemeans the model is able to handle the technicalities and complexities of the newlineenvironment under consideration at different levels...