Complex Dynamic Systems
- Corso del 1° Anno di Magistrale (1° Semestre).
- Docente: Chiara Mocenni.
- Link to Drive with Video Lectures
- moodle
- Contents and Program.
- Memory cards (to be used after you have studied, since there are some errors)
Remade Lectures:
I suggest you first read and watch (Video Lectures) the thoretical lessons, then the MATLAB ones, finally the exam example (Lecture 21), however i’m just a text, not a cop.
- Lecture 1:
- Lecture 2.
- Lecture 3.
- Lecture 4:
- CDS - Definition of ODE • Definition of a Solution • Definition of Flow • Dynamics • Definition of Phase Plane or Phase Space
- CDS - Qualitative vs Quantitative Analysis
- CDS - Theorem ‘Existence of Solutions’
- CDS - Vector Field
- CDS - Nullclines
- CDS - Linear 2D System • Example of Vector Fields
- CDS - Non-Linear 2D System • Example of Vector Fields • Definition of Coupled System
- Lecture 5:
- CDS - Example of a Phase Space • Pendulum Example
- CDS - Steady States • Classification of Steady States • Stable • Unstable • Marginally Stable • Attracting • Lyapunov Stable • Asympotically Stable
- CDS - Examples of Nullclines
- CDS - Eigenvalues and Eigenvectors
- CDS - Examples of Phase Space drawn from Eigenvalues and Eigenvectors • Nodes • Degenerate Node • Spirals • Circles
- Lecture 6:
- CDS - Examples of Phase Space drawn from Eigenvalues and Eigenvectors • Saddle • Marginally Stable Steady State
- CDS - Classification of Steady States in Continuos Systems
- CDS - Recap of Linear Systems
- CDS - Non-Linear Systems • Limit Cycles • omega-limit set • Poincaré-Bendixon Theorem
- CDS - Examples for a Bifurcation Diagram
- CDS - Linearization
- CDS - Hyperbolic Steady States • Hartman-Grobman Theorem
- CDS - Stable and Unstable Manifolds • Characterization of Homeomorphic and Non-homeomorphic Steady States
- Lecture 7. (MATLAB)
- Lecture 8:
- CDS - Examples for Eigenvalues and Eigenvectors in 2D
- CDS - Examples for Eigenvalues and Eigenvectors in 3D
- CDS - Bifurcation • Structural Stability • Bifurcation Value • Bifurcation Diagram
- CDS - Saddle-Node Bifurcation
- CDS - Transcritical Bifurcation
- CDS - Supercritical Pitchfork Bifurcation
- CDS - Subcritical Pitchfork Bifurcation
- Lecture 9. (MATLAB)
- Lecture 10:
- Lecture 11. (MATLAB)
- Lecture 12 ~ 13:
- Lecture 14. (MATLAB)
- Lecture 15:
- Lecture 18:
- Lecture 19:
- Lecture 20:
- Lecture 21. (written exam example)
- Lecture 22:
Topics of Choice
I was asked to bring a “topic of choice” (“argomento a piacere”) when discussing the “Master Seminar”, also the first question the professor asked me was a “topic of my choice”, so I suggest you bring one as well, to start the oral exam (if you take one) with the right foot.
Master Seminar
Exercises:
All Exercises ⇒ General Solutions.
- All types of exercises:
- Dynamical System with Parameters
- Discrete System with Parameters
- Steady States
- Jacobian Matrix
- Coupling Term
- Bifurcations
- Describe the System
- Describe the Dynamics
- Summarize the Results in a Single Sentence
- Simulation
- Chaotic System
- Chaotic Dynamic
- Discrete Maps
- Hartman-Grobman Theorem
- Why is a Steady State Asymptotically Stable
- Possible Situations of a Non-Linear Dynamical System
- Smallest Dimension Required to Exibit Oscillations
All My Notes
For the best experience in reading these and all other notes, and also if you wish to EDIT them, do as follows:
- Install Obsidian, or another markdown editor.
- Go to the Github link of this or another note
- Download all the repo or if you know git just the ‘content/’ folder
- Extract just the ‘content/’ folder from the repo zip file
- Open Obsidian >> Menage Vaults >> Open Folder as Vault >> and select the ‘content/’ folder you just extracted
PLEASE NOTE:
- These notes were not revised by the professors, so take all of them with a grain of salt.
- However if you download them since they are made in markdown you can EDIT them, please do so.
- If you edit and “upgrade” them, please pass the new ones to the other students and professors.
Here are all the links to my notes:
- Github: UNISI-Sensors-and-Microsystems-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Sensors-and-Microsystems-Obsidian-Quartz-Publish. - Github: UNISI-Complex-Dynamic-Systems-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Complex-Dynamic-Systems-Obsidian-Quartz-Publish. - Github: UNISI-Discrete-Event-Systems-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Discrete-Event-Systems-Obsidian-Quartz-Publish. - Github: UNISI-System-Identification-and-Data-Analysis-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-System-Identification-and-Data-Analysis-Obsidian-Quartz-Publish. - Github: UNISI-Multivariable-NonLinear-and-Robust-Control-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Multivariable-NonLinear-and-Robust-Control-Obsidian-Quartz-Publish. - Github: UNISI-Artificial-Intelligence-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Artificial-Intelligence-Obsidian-Quartz-Publish. - Github: UNISI-Human-Centered-Robotics-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Human-Centered-Robotics-Obsidian-Quartz-Publish. - Github: UNISI-Machine-Learning-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Machine-Learning-Obsidian-Quartz-Publish. - Github: UNISI-Bioinformatics-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Bioinformatics-Obsidian-Quartz-Publish. - Github: UNISI-Network-Optimization-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Network-Optimization-Obsidian-Quartz-Publish. - Github: UNISI-Mathematical-Methods-for-Engineering-Obsidian-Quartz-Publish;
Quartz Publish: UNISI-Mathematical-Methods-for-Engineering-Obsidian-Quartz-Publish.