Mathematical Topics on Modelling Complex Systems: In Memory of Professor Valentin Afraimovich

This book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts.

The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal-semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods.

The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions.

The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection-diffusion equation with generalized polynomials

The fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations.

The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.

本書探討了近年來對現實世界複雜系統的理論研究和數學建模的最新發展，分為四個部分。

第一部分專注於工程和社會科學研究案例中的設計和分析的數學工具。我們討論了非線性化學過程中的周期性演變、振動壓實系統及其行為、由銀納米線和氧化鋅納米棒製成的不同類型的金屬-半導體自組裝樣品。

第二部分專注於關鍵事件、氣候變化和強韌緊急情況的數學描述和建模。在三個章節中，我們考慮了一個具有內生碳強度的氣候-經濟模型，以及德黑蘭證券交易所在國際制裁下的行為。

第三部分專注於分數動態和分數控制問題。我們討論了變階分數最優控制問題的新型運算矩陣技術，以及具有廣義多項式的非線性變階時間分數對流-擴散方程。

第四部分涉及微分和積分微分方程中的可解性和反問題。

本書有助於更好地理解非線性動力學中的機制和現象，並發展相應的數學理論，以將非線性設計應用於實際工程。適合數學家、物理學家、複雜系統科學家、IT專家、土木工程師、數據科學家和城市規劃師閱讀。

Dr. J.A. Tenreiro Machado was born at 1957. He graduated with 'Licenciatura' (1980), Ph.D. (1989) and 'Habilitation' (1995), in Electrical and Computer Engineering at the University of Porto. During 1980-1998, he worked at the Dept. of Electrical and Computer Engineering of the University of Porto. Since 1998, he works at the Institute of Engineering, Polytechnic Institute of Porto, Dept. of Electrical Engineering. His research interests are complex systems, nonlinear dynamics, fractional calculus, modelling, control, entropy, evolutionary computing, genomics, robotics and intelligent transportation systems.

Dr. Dimitri Volchenkov obtained his Ph.D. in Theoretical Physics in the Saint Petersburg State University (Russia) and habilitated in the CNRS Centre de Physique Theorique (Marseille, France). He is Associate Professor of Mathematics and Statistics at the Texas Tech University (USA) and Professor Risk Assessment and Data Science at the Sichuan University of Science and Engineering (China). His research interests are the science of complexity and interdisciplinary physics ranging from the stochastic nonlinear dynamics to plasma turbulence, to urban spatial networks, and their impact on poverty and environments, analysis of complex networks, data analysis of economic, inequality and politics data, big data analytics, survival analysis, modelling of evolutionary biology and ecology.

Dr. J.A. Tenreiro Machado於1957年出生。他在波爾圖大學獲得電機與電腦工程的學士學位（1980年），博士學位（1989年）和博士後資格（1995年）。在1980年至1998年期間，他在波爾圖大學的電機與電腦工程系工作。自1998年以來，他在波爾圖理工學院工程學院的電機工程系工作。他的研究興趣包括複雜系統、非線性動力學、分數微積分、建模、控制、熵、演化計算、基因組學、機器人學和智能交通系統。

Dr. Dimitri Volchenkov在聖彼得堡國立大學（俄羅斯）獲得理論物理學博士學位，並在法國馬賽的CNRS理論物理中心獲得博士後資格。他是德克薩斯科技大學（美國）的數學與統計學副教授，以及四川科技大學（中國）的風險評估與數據科學教授。他的研究興趣涵蓋從隨機非線性動力學到等離子體湍流、城市空間網絡及其對貧困和環境的影響、複雜網絡分析、經濟、不平等和政治數據的數據分析、大數據分析、生物演化和生態建模等跨學科物理學領域。