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.
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.
Provides methods
for mathematical models with switching, thresholds, and impulses, each of
particular importance for discontinuous processes
Includes
qualitative analysis of behaviors on Tumor-Immune Systems and methods of
analysis for DNA, neural networks and epidemiology
Introduces new
concepts, methods, and applications in nonlinear dynamical systems covering
physical problems and mathematical modeling relevant to molecular biology,
genetics, neurosciences, artificial intelligence as well as classic problems in
mechanics, astronomy, and physics
Demonstrates
mathematic modeling relevant to molecular biology, genetics, neurosciences,
artificial intelligence as well as classic problems in mechanics,
astronomy, and physics