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"Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts low, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems."

"Avian flu dan swine flu merupakan penyakit pernapasan menular yang disebabkan oleh virus influenza yang menyerang hidung, tenggorokan, bronkus, dan terkadang paru-paru. Infeksi yang disebabkan mulai dari penyakit ringan, berat, dan bahkan kematian. Peristiwa genetic reassortment dapat membentuk suatu virus baru yang merupakan gabungan kemampuan dari virus avian flu dan swine flu yang disebut mutant-type flu. Pengobatan dengan obat antiviral digunakan untuk proses penyembuhan ketiga penyakit tersebut. Untuk mengetahui model penyebaran penyakit tersebut, digunakan model epidemi SIR beserta analisa titik keseimbangan, kestabilan, dan basic reproduction number R0 dengan metode pendekatan Next Generation Matrix NGM. Pendekatan pada model menggunakan model deterministik dengan sistem persamaan diferensial berdimensi tujuh. Kajian analitik dan numerik digunakan untuk interpretasi pada hasil yang diberikan oleh model. Dari hasil kajian tersebut, diperoleh 3 nilai basic reproduction number yang menjadi faktor penentu bertahannya penyakit avian flu dan swine flu di lingkungan.

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Avian flu and swine flu are respiratory infectious diseases caused by influenza viruses that attack the nose, throat, bronchus, and sometimes the lungs. Infections caused from mild, severe, and even death. The genetic reassortment can produce a new virus that is a combination of avian flu and swine flu viruses called mutant type flu. Treatment with antiviral drugs is used for the healing process of these diseases.

To find out the model of the spread disease, SIR epidemic model used with the analysis of the equilibrium point, stability, and basic reproduction number R0 with the Next Generatin Matrix NGM approach. The model approach uses a deterministic model with a seven dimensional differential equation system. Analytic and numerical studies are used for the interpretation of the results provided by the model. From the result of the study, we get 3 values of basic reproduction number which becomes the determinant factor for the survival of avian flu and swine flu diseases in the environtment."