@article{1435106,
      recid = {1435106},
      author = {Church, Kevin E. M., and Liu, Xinzhi,},
      title = {Bifurcation theory of impulsive dynamical systems /},
      pages = {1 online resource (xvii, 388 pages) :},
      abstract = {This monograph presents the most recent progress in  bifurcation theory of impulsive dynamical systems with time  delays and other functional dependence. It covers not only  smooth local bifurcations, but also some non-smooth  bifurcation phenomena that are unique to impulsive  dynamical systems. The monograph is split into four  distinct parts, independently addressing both finite and  infinite-dimensional dynamical systems before discussing  their applications. The primary contributions are a  rigorous nonautonomous dynamical systems framework and  analysis of nonlinear systems, stability, and invariant  manifold theory. Special attention is paid to the centre  manifold and associated reduction principle, as these are  essential to the local bifurcation theory. Specifying to  periodic systems, the Floquet theory is extended to  impulsive functional differential equations, and this  permits an exploration of the impulsive analogues of  saddle-node, transcritical, pitchfork and Hopf  bifurcations. Readers will learn how techniques of  classical bifurcation theory extend to impulsive functional  differential equations and, as a special case, impulsive  differential equations without delays. They will learn  about stability for fixed points, periodic orbits and  complete bounded trajectories, and how the linearization of  the dynamical system allows for a suitable definition of  hyperbolicity. They will see how to complete a centre  manifold reduction and analyze a bifurcation at a  nonhyperbolic steady state.},
      url = {http://library.usi.edu/record/1435106},
      doi = {https://doi.org/10.1007/978-3-030-64533-5},
}