From local bifurcations to global dynamics: Hopf systems from the applied perspective

DOI10.1007/978-3-030-70982-2_5OpenAlexW3196997017MaRDI QIDQ2097852

Yanyan Li

Publication date: 15 November 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-70982-2_5

zbMATH Keywords

Lorenz systemdelay-differential equationsRössler systemShilnikov theoremHopf bifurcation theorem

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Dynamical aspects of attractors and their bifurcations (37G35) Bifurcation theory of functional-differential equations (34K18) Complex (chaotic) behavior of solutions to functional-differential equations (34K23)

Cites Work

• Unnamed Item
• Chaotic attractors of an infinite-dimensional dynamical system
• Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov
• Time delays and chaos in two competing species
• On lags and chaos in economic dynamic models
• Criterion of Hopf bifurcations without using eigenvalues
• Coefficient criterion for four-dimensional Hopf bifurcations: a complete mathematical characterization and applications to economic dynamics
• Dynamic complexity in a Keynesian growth-cycle model involving Harrod's instability
• Shilnikov chaos in the Lucas model of endogenous growth
• The Lorenz equations: bifurcations, chaos, and strange attractors
• An equation for continuous chaos
• Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags
• Deterministic Nonperiodic Flow
• Oscillation and Chaos in Physiological Control Systems
• Shil'nikov's theorem-a tutorial