A course given by Franco Bagnoli at the Technocal University of Gdansk, 26-30 March 2012 (15 hours)
What is computation. Von Neumann architecture. Artificial Intelligence. Emerging computation. Control theory. Extendend systems.
Dynamical systems in 1D. Phase space. Flow on the line. Fixed points. Stability. Bifurcation diagram. Saddle-node bifurcation, Trasncritical bifurcation. Supercritical pitchfork bifurcation. Subcritical pitchfork bifurcation. 2D systems. Phase space and vector field. Nullclines. Fixed points. Stability, saddle, nodes and spirals. Limit cycles.
Limit cycles. Supercritical Hopf bifurcation. Subcritical Hopf bifurcation. Quasiperiodicity. Time-series. Fourier spectrum. Chaos. The Lorenz attractor. Lyapunov exponents. Poincaré sections. Maps. The logistic map. The bifurcation diagram. Period doubling and intermittency routes to chaos.
Extendend systems: partial differential equations, finite elements, coupled maps, cellular automata. Transition function. Trajectories. Attractors. Transients, period of limit cycles. Basin of attraction and phase space. Lyapunov spectrum, and the thermodynamic limit. Conservative and dissipative systems. Kolmogorov-Sinai entropy. Synchronization and Lyapunov exponents. Pinching synchronization of coupled maps.
Stochastic cellular automata. Markow processes. Relaxation to equilibrium. The Domany-Kinzel model. Phase transitions. Small-world effect http://en.wikipedia.org/wiki/Watts_and_Strogatz_model. Network theory http://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model Chaotic transitions induced by topology.
Genes and replicators. Genotype and phenotype. The fitness landscape. The Fisher theorem and the gause principle. Quasispecies. The influence of mutations. The problem of coexistence. Competition and speciation in smooth fitness landscapes. Muller's ratches and the mutational mettdown. Sex and recombination. Evolution of sexual replication. The sexual run-out: sexual ornaments. Brain as a sexual ornament in humans. Consequences of big brains. Brain and group size. The social brain. Game theory. Evolution of cooperation.
All material: http://born.de.unifi.it/~franco/UnconventionalComputing/ see also