Hasil Pencarian  ::  Simpan CSV :: Kembali

"Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point."

"Pada tesis ini dibahas mengenai sistem predator-prey dengan tingkat kelahiran prey jauh lebih kecil dibandingkan tingkat kematian predator dan mengasumsikan bahwa populasi prey terbatas, sehingga ditambahkan faktor kapasitas lingkungan ke populasi prey. Karena perbedaan rentang waktu regenerasi antara predator dan prey relatif tinggi, sistem memiliki struktur fast-slow. Struktur fast-slow pada model dianalisis dengan menggunakan geometric singular perturbation theory (GSPT) yang membagi sistem menjadi fast subsystem dan slow subsystem. Dalam tesis ini, dipelajari keberadaan solusi ekuilibrium dan stabilitasnya, dan juga perilaku solusi di sekitar critical manifold. Selanjutnya, dengan menggunakan fungsi entry-exit diperoleh hubungan antara solusi fast subsystem dan slow subsystem secara analitis.

---

In this thesis we discuss the predator-prey system with the birth rate of the prey is much smaller compared to the predator mortality rate where it is assumed that the population of prey is limited. Therefore, an environmental carrying capacity factor is added to the prey population. Due to the difference in regeneration’s timescales between predator and prey, some solutions of the system may have a fast-slow structure. The fast-slow structure of the model is analyzed using the geometric singular perturbations theory (GSPT) which divides the system into fast and slow subsystem. In this thesis, we study the existence of the equilibrium solutions and their stability, and also the behaviour of the solutions near critical manifold. Furthermore, using an entry-exit function we obtain the connection between the solutions of the slow subsystem and the fast subsystem analytically."