Asymptotic models and methods in complex systems dynamics (General approach) Available to Purchase

The paper is concerned with the different aspects of mathematical modelling and analysis in dynamics of complex non‐linear systems, that are generated by applied problems of engineering practice. Main aims are the problems of optimal (in some sense) mechanical‐mathematical modelling and the regular schemes of decomposition. The critical step in the use of mathematics for solving complex engineering problems is the building of a suitable mathematical model, that, generally speaking, is the result of combining the mathematical formalized procedures as well as heuristic (non‐formalized) manners (conjunction of rigorous science and free art). This work advocates a novel approach to the building process of mathematical models, presenting an overview of concepts and techniques needed for modelling, via comprehension of modelling problem as singularly perturbed one. Here uniform methodology, based on methods of Lyapunov theory, Perturbations theory [Asymptotic method in theory of non‐linear oscillations (1963)] in accordance with Stability postulate and Singularity postulate is developed. This asymptotic approach (called – LPSS approach) allows to elaborate the general conception of the modelling; to determine the conditions of qualitative equivalence between full model and simplified model. As applications, the different examples of concrete physical nature are considered.