Differential Models: Dynamical Systems with Perturbations

Area 01 – Scienze matematiche e informatiche

The purpose of the present Monograph is to investigate the qualitative characteristics of the solutions of the ordinary (partial) systems of differential equations perturbed by impulse and parametric influence on some hypersurfaces (fixed moments of time). The method of integral inequalities for discontinuous functions has been developed. The new results in the theory of impulsive systems are obtained. The problems of stability by Lyapunov and practical stability by Chetaev for impulsive systems of differential and integro-differential equations are investigated. New results in the theory of Global Attractor for continuous and discontinuous right–hand side of systems are formulated. The task of optimal controlling for objects with distributed parameters discribed by non–linear differential equations of elliptical, parabolic, hyperbolic types are considered. The book is devoted to students of higher educational institutions, postgraduates, doctorants of Physics and Mathematics specialities of Universities, engineering Institutes as well as for research engineers who use the methods of qualitative theory of differential equations in their researches.Gerardo Iovane is Professor of Mathematics at the Engineering Faculty of the University of Salerno and teach Biometry and Identification for the course of Computer Science at the Faculty of MM.FF.NN. Sciences at the University of Messina. After the laurea degree in Physics, with nuclear and subnuclear address, he has made a Master at the CERN of Geneva and has achieved two PhD respectively in Physics and in Mathematics. At present he deals with mathematical methods and models applied to exact sciences, with particular regard to the themes connected with the study of dynamic systems, complexity, security and biometry with new image processing methodologies. In the Academic Year 2006–2007 he accomplished the title of the “Istituto Alti Studi della Difesa” and is collaborating both with various structures of the “Ministero della Difesa” and with the Police. He is author of about one hundred and fifty scientific articles on International journals and conference contributions and books. He is editor of ten international journals.Borysenko S.D. (born, 1956), doctor of science, is Full professor at Department of Differential Equations–Physical–Mathematical Faculty of National Technical University of Ukraine “Kyiv Polytechnic Institute”, Corresponding Member Academia Peloritana dei Pericolanti (Messina). He found the theory of integro–sum inequalities (impulsive integral inequalities) for investigating qualitative analysis the system of differential equations with impulse perturbations. Author of about 150 scientific works, also 11 monograph and manuals, he is Editor of 3 journals : “Naukovi Visti NTUU”, “Mathematical Methods, Physical Models and Simulation in Science&Technology”, “Transaction of Applied Mathematics and Nonlinear Models”. He is also Coordinator of International Agreement of scientific cooperation between National Technical University of Ukraine “KPI” and University of Salerno.

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