List of projects

1. List of projects Chiara Mocenni http://www.dii.unisi.it/~mocenni

2. Chemicalreactions Oscillations can arise in a macroscopic medium if the systemissufficiently far from the state of thermodynamicequilibrium (Nicolis and Prigogine, 1977). Brusselator stirred unstirred

3. Il modello Lotka-Volterra Ecological systems x = prey y = predator (x) = growth of prey  = mortality of predator p(x) = functionalresponse of the predator

4. Economicsystems Cournotcompetitionis an economic model used to describe an industrystructure in which companies compete on the amount of output theywill produce, whichthey decide on independently of eachother and at the same time. Itisnamedafter Antoine AugustinCournot(1801–1877). Ithas the followingfeatures: Thereis more thanonefirm and allfirms produce a homogeneousproduct, i.e. thereis no productdifferentiation Firms do not cooperate, i.e. thereis no collusion Firmshave market power, i.e. eachfirm's output decisionaffects the good'sprice The number of firmsisfixed Firms compete in quantities, and choosequantitiessimultaneously The firms are economicallyrational and actstrategically, usuallyseeking to maximize profit giventheir competitors' decisions Discrete time or continuous time nonlinearequations

5. Epidemicmodeling W. O. Kermack and A. G. McKendrickmodel • http://nrich.maths.org/4489 S: population of suceptibles I: populationifinfected R: population of recovered

6. Time seriesanalysis • Suppose thatyouonlyhave the recordings of some measurescorrelated to a state variable of a dynamicalsystem • You can estimate the level of chaoticity in the time series by calculatingsomeindicators, suchas the Lyapunovexponent • You can reconstructapproximately the originalsystem by usingdelayedcoordinates

7. Fractals The Mandelbrot set is the set of values of c in the complexplane for which the orbit of 0 under iteration of the complexquadraticpolynomial zn+1 = zn2 + c remainsbounded. Thatis, a complexnumber c is part of the Mandelbrot set if, whenstarting with z0 = 0 and applying the iterationrepeatedly, the absolutevalue of znremainsboundedhowever large ngets. Whataboutiterating the logisticmapinstead?

8. Matlab Toolbox • Development of some Matlabtools for the analysis of the bifurcations of nonlinearsystems

9. Billiardtable A billiardis a dynamicalsystem in which a particlealternatesbetweenmotion in a straight line and specular reflections from a boundary. When the particlehits the boundaryitreflects from itwithoutloss of speed. Whataboutsimulating and calculating the Lyapunovexponent of the trajectories?

10. Ott, Grebogi & Yorke Chaos control ..It is shown that one can convert a chaotic attractor to any one of a large number of possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter…

11. Complexity science: The elephant in the dark

12. Complexity science

13. Complex Networks

14. Reaction-diffusion systems dove time derivative lapplacian (diffusion)‏ u(x,y,t)concentration of a species, Ddiffusion coefficient, f(u,x,y,t)reaction term

15. Otherapplications • Brain dynamics • Double pendulum • . • . • .