Modules  Area  Type  Hours  Teacher(s)  
SISTEMI COMPLESSI  FIS/03  LEZIONI  54 

Students are expected to acquire: some knowledge of stochastic calculus and probability, chaos dynamics and of the relevant tools and models; some knowledge to the appropriate tools to approach complex systems;
Students are expected to acquire: some knowledge of stochastic calculus and probability, chaos dynamics and of the relevant tools and models; some knowledge to the appropriate tools to approach complex systems;
Students are expected to apply the learnt methods to a concrete case of interest. The emphasis will be on how the apply the learnt methodologies rather than on the results achieved in the application.
Methods:
Students are expected to apply the learnt methods to a concrete case of interest. The emphasis will be on how the apply the learnt methodologies rather than on the results achieved in the application.
Methods:
The student will be able to study and model some simple "complex system"
The student will be able to study and model some simple "complex system"
The student will be invited to apply to concrete cases some of the methodologies taught, throughout the lectures
The student will be invited to apply to concrete cases some of the methodologies taught, throughout the lectures
The student need to have the standard knowledge in maths and physics of a physics bachelor: calculus in many variables, knowledge of Fourier transform, classical physics (in particular, Hamiltonian mechanics), some background in classical thermodynamics.
The student need to have the standard knowledge in maths and physics of a physics bachelor: calculus in many variables, knowledge of Fourier transform, classical physics (in particular, Hamiltonian mechanics), some background in classical thermodynamics.
The lectures of Sistemi Complessi provide some of the background knowledge (stochastic differential equations) needed to attend the lectures of:
Sistemi complessi  Dinamiche Neurali
Biorobotica e sistemi complessi
Modellistica per sistemi complessi
and an introduction to chaos needed to attend the lectures of:
Dinamica nonlineare
The lectures of Sistemi Complessi provide some of the background knowledge (stochastic differential equations) needed to attend the lectures of:
Sistemi complessi  Dinamiche Neurali
Biorobotica e sistemi complessi
Modellistica per sistemi complessi
and an introduction to chaos needed to attend the lectures of:
Dinamica nonlineare
Delivery: face to face
Learning activities:
Attendance: Advised
Teaching methods:
Delivery: face to face
Learning activities:
Attendance: Advised
Teaching methods:
The course has a modular structure: 6 ECTS are devoted to general tools to study complex systems, like stochastic methods, chaotic dyamics etc.. The students then take an additional 3 ECTS modulus which applies the general tools to some complex systems. The modulus offered will depend on the specific academic year: this year it will mostly cover subjects on Econophysics
The general tools part of the course will cover topics like:
Brownian motion, Chapman Kolmogorov equation, Stable (Levy) distributions, Stochastic integration, Fokker Planck equation, Mean First Passage Time related problems, Path integral approach to stochastic processes; Chaotic dynamics both for conservative and dissipative flows, related tools (like Poincare maps and Lyapunov exponents), Fractals.
The course has a modular structure: 6 ECTS are devoted to general tools to study complex systems, like stochastic methods, chaotic dyamics etc.. The students then take an additional 3 ECTS modulus which applies the general tools to some complex systems. The modulus offered will depend on the specific academic year: this year it will mostly cover subjects on Econophysics
The general tools part of the course will cover topics like:
Brownian motion, Chapman Kolmogorov equation, Stable (Levy) distributions, Stochastic integration, Fokker Planck equation, Mean First Passage Time related problems, Path integral approach to stochastic processes; Chaotic dynamics both for conservative and dissipative flows, related tools (like Poincare maps and Lyapunov exponents), Fractals.
Gardiner, Handbook of stochastic methods
Reichl, The transition to chaos
Tabor, Chaos and integrability in nonlinear dynamics
Gardiner, Handbook of stochastic methods
Reichl, The transition to chaos
Tabor, Chaos and integrability in nonlinear dynamics
The exam will be in oral form. The student is expected to work on a small project during which he/she will apply the tools and methodologies taught in the lectures, and to prepare a small talk/script, which will be the basis from which the oral exam will be carried out
The exam will be in oral form. The student is expected to work on a small project during which he/she will apply the tools and methodologies taught in the lectures, and to prepare a small talk/script, which will be the basis from which the oral exam will be carried out