A growing number of both established and newly developed doctoral programs are focusing on the preparation of practitioners rather than career researchers. Professional doctorates such as the Doctor of Nursing Practice (DNP), Doctor of Education (EdD), Doctor of Pharmacy (PharmD), Doctor of Professional Studies (DProf or DPS), and the Doctor of Psychology (PsyD) are, in fact, just a few of the professional doctorates being offered today. Professional doctorates are the fastest growing segment of doctoral education. The nature of the dissertation and the process of completing a dissertation can be quite different in a professional practice doctoral program but there are few resources for both students and faculty involved in completing and mentoring such dissertations. This book was written specifically for students and faculty involved in professional practice dissertation work. It addresses both the tasks and procedures that professional practice dissertations have in common with dissertations in "research" doctoral programs as well as the tasks and issues that are more common in professional practice doctoral programs. For example, negotiating entry into applied settings and securing the cooperation of practicing professionals is covered, as are alternative models for the dissertation (e.g., the "three article dissertation" or "TAD"). The book also covers tasks such as getting IRB approval for applied dissertation research conducted in the field and how to propose and carry out studies based on applied and professional models of research. This book, written by three experienced mentors of professional practice dissertation students, is the comprehensive guide for both students and faculty.
When a dynamical system has a large number of parameters it is not possible to get a completely comprehensive picture of all the types of behavior that it may display and one must be content with surveying the system along various corridors of lower dimension. Using an example with three differential equations and six parameters it is shown how the available methods of singularity theory, bifurcation analysis, normal forms, etc. can be used to build up a picture of varied and interesting behavior. The model is a generalization of the Gray-Scott reaction scheme in a single stirred vessel to a two-phase reactor consisting of a reaction chamber and a reservoir communicating with each other through a semi-permeable membrane. Two forms exist according as to whether A is fed to the reactor and B to the reservoir or vice-versa, and show interesting differences of behavior. Both models undergo Hopf bifurcations, pitchfork transitions, have homoclinic orbits, take the period doubling route to chaos and one gets there by intermittency.
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