Virtually any advance in disease dynamics requires a sophisticated mathematical approach in order to map out the parameters that drive the system. This book exploits some of the fundamental theory of dynamical systems and applies them to biological and social sciences. Topics include the asymptotic stability of almost periodic systems; modeling and vibration-based system identification and damage inspection of flexible structures; the stability and persistence of dynamical systems using Lyapunov functions; Krylov and Schur subspaces in construction of prediction error filter and its computational complexity and performance comparison, parametric resonance and homoclinic chaos in a Bullard-type dynamo; and birhythmicity, synchonization and chaos in an enzyme-substrate reaction with ferroelectric behavior. Biological applications include the local stability of an age-structured Hepatitis B model, the dynamics of a predator-prey model, avian influenza, tuberculosis, malaria and HIV-TB co-dynamics. A possible application of nonlinear dynamical systems in social sciences is also investigated.
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