Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods

DOI10.1016/j.amc.2015.10.009zbMath1410.39012OpenAlexW2176862534MaRDI QIDQ668564

Jian Shi, Chenqi Mou, Wei Niu

Publication date: 19 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.10.009

zbMATH Keywords

symbolic computationdiscrete dynamical systemflip-Neimark-Sacker bifurcationfold-Neimark-Sacker bifurcation

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items

Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination, Analysis of Snapback Repellers Using Methods of Symbolic Computation, Algebraic Analysis of Bifurcations and Chaos for Discrete Dynamical Systems

Uses Software

• SYNRAC
• DISCOVERER

Cites Work

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• Stability analysis for discrete biological models using algebraic methods
• New bifurcation critical criterion of flip-Neimark-Sacker bifurcations for two-parameterized family of \(n\)-dimensional discrete systems
• A complete algorithm for automated discovering of a class of inequality-type theorems
• Local feedback stabilization and bifurcation control. I. Hopf bifurcation
• The stability and control of discrete processes
• Elimination methods
• Elements of applied bifurcation theory.
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Some discrete-time SI, SIR, and SIS epidemic models
• Testing stability by quantifier elimination
• Deciding Hopf bifurcations by quantifier elimination in a software-component architecture
• Bistability and an Allee effect as emergent consequences of stage-specific predation
• Feedback control of Hopf-Hopf interaction bifurcation with development of torus solutions in high-dimensional maps
• Solving parametric polynomial systems
• Testing sign conditions on a multivariate polynomial and applications
• Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems
• Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits
• Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems
• THE FOLD-FLIP BIFURCATION
• THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS
• A package for solving parametric polynomial systems
• BIFURCATION CONTROL: THEORIES, METHODS, AND APPLICATIONS
• Numerical Normal Forms for Codim 2 Bifurcations of Fixed Points with at Most Two Critical Eigenvalues
• Generalized Hénon Map and Bifurcations of Homoclinic Tangencies