Normal forms, melnikov functions and bifurcations of limit cycles / Maoan Han, Pei Yu

This excellent book advances the theory of Limit Cycles—isolated periodic orbits that are sometimes referred to as self-sustained oscillations in the literature. Here the authors' focus is on the bifurcations of limit cycles, thoroughly and extensively analyzed in the three classical scenarios: (1) Hopf bifurcation from centers or focus using the theory of normal forms; (2) Poincaré bifurcation from closed orbits using the method of Melʹnikov functions and (3) separatrix bifurcation from homoclinic or heteroclinic loops, also using the method of Melʹnikov functions. The literature on limit cycles is quite substantial. This book stands out with worked-out examples galore and efficient and accessible algorithms on classical subjects such as the computation of normal forms, as well as on recent developments of Melʹnikov functions, including bifurcations in equivariant systems. The authors aim at shedding new light on "old'' settled results as well as introducing recent advances in the field. The book achieves both handsomely, through a highly readable and convincing exposition that harnesses the power of modern computational tools such as Computer Algebra Systems (CAS), in particular MAPLE. ... (MSN)