List of projects Chiara Mocenni http www dii

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

Chemical reactions Oscillations can arise in a macroscopic medium if the system is sufficiently far from the state of thermodynamic equilibrium (Nicolis and Prigogine, 1977). Brusselator stirred unstirred

Il modello Lotka-Volterra Ecological systems x = prey y = predator (x) = growth of prey = mortality of predator p(x) = functional response of the predator

Economic systems Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot (1801– 1877). It has the following features: There is more than one firm and all firms produce a homogeneous product, i. e. there is no product differentiation Firms do not cooperate, i. e. there is no collusion Firms have market power, i. e. each firm's output decision affects the good's price The number of firms is fixed Firms compete in quantities, and choose quantities simultaneously The firms are economically rational and act strategically, usually seeking to maximize profit given their competitors' decisions Discrete time or continuous time nonlinear equations

Epidemic modeling W. O. Kermack and A. G. Mc. Kendrick model S: population of suceptibles I: population if infected R: population of recovered • http: //nrich. maths. org/4489

Time series analysis • Suppose that you only have the recordings of some measures correlated to a state variable of a dynamical system • You can estimate the level of chaoticity in the time series by calculatingsome indicators, such as the Lyapunov exponent • You can reconstruct approximately the original system by using delayed coordinates

Fractals The Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn 2 + c remains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets. What about iterating the logistic map instead?

Matlab Toolbox • Development of some Matlab tools for the analysis of the bifurcations of nonlinear systems

Billiard table A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. What about simulating and calculating the Lyapunov exponent of the trajectories?

Chaos control Ott, Grebogi & Yorke . . 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…

Complexity science: The elephant in the dark

Complexity science

Complex Networks

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

Other applications • • • Brain dynamics Double pendulum. . .