Cycles in continuous and discrete dynamical systems : computations, computer-assisted proofs, and computer experiments
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Summary
Application of the qualitative theory of dynamical systems, special analytical methods, and modern mathematical packages has helped to advance considerably in calculation of bifurcation values and to define numerically fourteen biforcation values of the DPLL’s parameter.
- Type
- article
- Published
- 2009-01-01
- Cited by
- 2
- References
- 72
- Access
- Open access
- OpenAlex
- https://openalex.org/W34839643
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:115203284
Keywords
Mathematical proof, Computer science, Computation, Calculus (dental), Theoretical computer science
References
- Limit Cycles of Differential Equations
- COMPUTATION OF LYAPUNOV QUANTITIES
- Dynamics of One-Dimensional Maps
- Bifurcation Control: Theory and Applications
- Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications
- Equations of Phase-Locked Loops: Dynamics on Circle, Torus and Cylinder
- DSP Processor Fundamentals: Architectures and Features
- Strange attractors and classical stability theory
- Chaotic Electronics in Telecommunications
- Theory of Oscillators
- Methods of qualitative theory in nonlinear dynamics
- PERIOD DOUBLING BIFURCATION IN DISCRETE PHASE-LOCKED LOOPS
- Ordinary differential equations and smooth dynamical systems
- Phase-locked loops
- Chaos in voltage-mode controlled DC drive systems
- Stability Analysis of an Nth Power Digital Phase-Locked Loop - Part I: First-Order DPLL
- Twelve Limit Cycles in a cubic Case of the 16TH Hilbert Problem
- Exact Solutions to the Feigenbaum Renormalization-Group Equations for Intermittency
- An Explicit Expression of the First Liapunov and Period Constants with Applications
- Chaos and bifurcation in a third-order digital phase-locked loop
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