1. Introduction 2. Conundrums 3. Anatomy 4. Physiology 5. Misrepresentation of the nonmonotonic nonlinear dynamics 6. Conceptual momentum of one-dimensional push-pull dynamics 7. Acquiring and analyzing nonmonotonic nonlinear dynamics 8. Nonmonotonic nonlinear dynamical modeling 9. Networks of nonmonotonic nonlinear oscillators Appendix A. Deep dive into neurophysiological epistemology Appendix B. Chance, randomness, and incompleteness Appendix C. Unpredictability, dependence on initial conditions and self-organization Appendix D. Information theory