Modelling Order and Disorder

Modelling Order and Disorder: Integro-Differential Nonlinear Equations provides an overview of a general mathematical structure: integro-differential nonlinear equations. This mathematical structure provides a unified approach to model complex systems in social sciences, economics, biology, medicine, and other quantitative disciplines. The general aim of the book is to reflect possible organization and disorganization phenomena in the applied sciences, as well as to focus on non-local interactions. Features - Applications to social, biological, and physical phenomena - Suitable for researchers and post-graduate students - Open questions and perspectives on future avenues of research

Miroslaw Lachowicz is Full Professor of Mathematics at the University of Warsaw. From 2016-2024, he served as the Chairman of the Scientific Committee of the Institute of Applied Mathematics and Mechanics. He is a Member of Editorial Boards: e.g. Mathematical Methods in the Applied Sciences, Mathematical Biosciences and Engineering, Letters in Biomathematics, Opuscula Mathematica. His research interests are Integro-differential Equations, Singularly Perturbed Problems, Markov Processes, Applications in Life and Social Sciences, Relationships between Mathematics and the Humanities. He has numerous scientific contacts, especially with universities in Italy and South Africa. He was an honorary professor at the University of KwaZulu-Natal in Durban, and he also spent some time at the Universities of Pretoria and Stellenbosch. He also travelled to numerous institutions in Europe and Japan.

Preface Acknowledgements 1 Introduction 2 Basic Mathematical Structures 3 Preliminary results 4 Constant interaction rate 5 Non-constant kernel of interaction 6 Small range of interactions 7 PDE limits 8 Equilibrium solutions 9 Microscopic scale 10 Diauxic growth 11 Discrete states 12 Space non-local models 13 Some applications 14 Conclusion Concluding proverb Bibliography Index