https://mklab.gr/ Mon, 19 Oct 2026 10:35:05 +0000 MyBB https://mklab.gr/showthread.php?tid=2110 Wed, 23 Sep 2026 22:58:29 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2110 Data-Driven Methods for Dynamic Systems by Jason J. Bramburger is a 2024 SIAM book that introduces modern data-driven techniques for analyzing and modeling dynamical systems. Its central theme is the combination of classical dynamical-systems mathematics with computational methods from data science and machine learning. The book covers dynamic mode decomposition (DMD), the Koopman operator, sparse/nonlinear modeling, polynomial optimization, neural networks, and autoencoders, showing how these tools can extract information about differential equations and time-dependent phenomena directly from experimental or simulated data.

A major message is that machine learning does not simply replace traditional mathematical modeling; instead, it can complement it by discovering useful representations, forecasting dynamics, and extracting system-level properties from data. The book discusses the limitations of purely linear approaches such as DMD and then introduces nonlinear methods and neural networks capable of better generalization. 

It also uses Koopman-operator methods and polynomial/semidefinite optimization to study complex systems without necessarily constructing an explicit model. Numerous MATLAB scripts and Jupyter notebooks accompany the examples, making the book particularly practical for graduate students and researchers working at the intersection of dynamical systems, differential equations, applied mathematics, and AI/data science.

BOOK]]> Data-Driven Methods for Dynamic Systems by Jason J. Bramburger is a 2024 SIAM book that introduces modern data-driven techniques for analyzing and modeling dynamical systems. Its central theme is the combination of classical dynamical-systems mathematics with computational methods from data science and machine learning. The book covers dynamic mode decomposition (DMD), the Koopman operator, sparse/nonlinear modeling, polynomial optimization, neural networks, and autoencoders, showing how these tools can extract information about differential equations and time-dependent phenomena directly from experimental or simulated data.

A major message is that machine learning does not simply replace traditional mathematical modeling; instead, it can complement it by discovering useful representations, forecasting dynamics, and extracting system-level properties from data. The book discusses the limitations of purely linear approaches such as DMD and then introduces nonlinear methods and neural networks capable of better generalization. 

It also uses Koopman-operator methods and polynomial/semidefinite optimization to study complex systems without necessarily constructing an explicit model. Numerous MATLAB scripts and Jupyter notebooks accompany the examples, making the book particularly practical for graduate students and researchers working at the intersection of dynamical systems, differential equations, applied mathematics, and AI/data science.

BOOK]]> https://mklab.gr/showthread.php?tid=1350 Sun, 26 Jul 2026 03:21:45 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1350
Nonlinear Dynamics and Chaos: 
With Applications to Physics, Biology, Chemistry, and Engineering
BY Steven H. Strogatz

Summary

** Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Steven H. Strogatz** is a comprehensive introduction to the fascinating world of nonlinear systems, chaos theory, and dynamical models. The book explains how simple mathematical rules can produce complex, unpredictable behaviour, covering topics such as fixed points, stability, bifurcations, oscillations, limit cycles, strange attractors, and chaotic motion. Strogatz develops the subject gradually, combining rigorous mathematics with intuitive explanations and real-world examples from fields including physics, biology, chemistry, and engineering. 

Through models such as population growth, chemical reactions, mechanical oscillators, and fluid dynamics, the book shows how nonlinear interactions shape many natural phenomena. It is especially valued for making advanced concepts accessible without sacrificing mathematical depth, using clear diagrams, applications, and problem-solving approaches. 

The central message is that complexity and unpredictability often emerge not from complicated causes but from simple systems interacting in nonlinear ways. Overall, it is considered one of the most influential modern textbooks on dynamical systems and chaos, suitable for advanced undergraduate students, researchers, and anyone interested in understanding the mathematics behind complex behaviour.


BOOK]]>
Nonlinear Dynamics and Chaos: 
With Applications to Physics, Biology, Chemistry, and Engineering
BY Steven H. Strogatz

Summary

** Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Steven H. Strogatz** is a comprehensive introduction to the fascinating world of nonlinear systems, chaos theory, and dynamical models. The book explains how simple mathematical rules can produce complex, unpredictable behaviour, covering topics such as fixed points, stability, bifurcations, oscillations, limit cycles, strange attractors, and chaotic motion. Strogatz develops the subject gradually, combining rigorous mathematics with intuitive explanations and real-world examples from fields including physics, biology, chemistry, and engineering. 

Through models such as population growth, chemical reactions, mechanical oscillators, and fluid dynamics, the book shows how nonlinear interactions shape many natural phenomena. It is especially valued for making advanced concepts accessible without sacrificing mathematical depth, using clear diagrams, applications, and problem-solving approaches. 

The central message is that complexity and unpredictability often emerge not from complicated causes but from simple systems interacting in nonlinear ways. Overall, it is considered one of the most influential modern textbooks on dynamical systems and chaos, suitable for advanced undergraduate students, researchers, and anyone interested in understanding the mathematics behind complex behaviour.


BOOK]]>