Mathematical Modeling and Applications in Nonlinear Dynamics

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

Introduction.- Mathematical Neuroscience: from neurons to networks.- Jupiters belts, our Ozone holes, and Degenerate tori.- Analytical solutions of periodic motions in time-delay systems.- DNA elasticity and its biological implications.- Epidemiology, dynamics, control and multi-patch mobility.- Exponential dichotomy and existence of almost periodic solutions for impulsive evolution .- equations.- Pseudo almost periodic solutions for a class of differential equations.- Effect of the Delay of the Immune Response on the Qualitative Behaviors on Tumor-Immune System.- Synchronization of the integrate-and-fire biological models with continuous/ discontinuous couplings.- Stability and Hopf Bifurcation Analysis of Lengyel-Epstein Reaction-Diffusion Model.- On the second Peskin conjecture solution.

Albert C.J. Luo is a Professor in the Department of Mechanical and Industrial Engineering, South Illinois University Edwardsville, Edwardsville, IL USA. Hüseyin Merdan is a Professor in the the
Department of Mathematics, TOBB University of Economics and Technology, Ankara, TURKEY.