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4. Orbits of Autonomous Systems

DOI: 10.1016/s0076-5392(08)60606-2
  • Mathematics


Publisher Summary This chapter discusses orbits of autonomous systems. The ordinary differential equation that does not explicitly contain an independent variable is called an “autonomous system.” Equations such as the van der Pol equation are familiar examples of autonomous systems. These equations can be rewritten in the form of the first-order systems. An autonomous system always admits of a family of parallel trajectories whose projection is a single orbit—in fact, the orbits are used more often than the trajectories in studying autonomous systems. The chapter also discusses closed orbits and continuity of orbits. In the theory of autonomous oscillations, the principal subjects are the periodic solutions of the autonomous system. The chapter concludes with a discussion of the critical points of autonomous systems.

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