Applied Nonautonomous and Random Dynamical Systems: Applied Dynamical Systems

1 Introduction.- 2 Autonomous dynamical systems.- 2.1 Basic Stability Theory.- 2.2 Attractors. - 2.3 Applications. - 2.3.1 Application to ecology: a chemostat model.- 2.3.2 Application to epidemiology: the SIR model.- 2.3.3 Application to climate change: the Lorenz-84 model.- 3 Nonautonomous dynamical systems.- 3.1 Formulations of nonautonomous dynamical systems.- 3.1.1 Process formulation.- 3.1.2 Skew product flow formulation.- 3.2 Nonautonomous Attractors.- 3.2.1 Nonautonomous attractors for processes.- 3.2.2 Nonautonomous attractors for skew product flows.- 3.3 Applications.- 3.3.1 Nonautonomous chemostat model.- 3.3.2 Nonautonomous SIR model.- 3.3.3 Nonautonomous Lorenz-84 model.- 4 Random dynamical systems.- 4.1 Noise is present almost everywhere.- 4.2 Formulation of Random Dynamical System and Random Attracto.- 4.2.1 Some properties of the random attractor.- 4.2.2 Generation of random dynamical systems.- 4.2.3 A brief introduction to stochastic differential equations.- 4.2.4 Global asymptotic behavior of SDEs: conjugation of RDS.- 4.3 Applications.- 4.3.1 Random chemostat.- 4.3.2 Random and stochastic SIR.- 4.3.3 Stochastic Lorenz models.- 4.4 Stabilization of dynamical systems. References