What are some recent advances in the use of bifurcation analysis and numerical methods for modelling complex dynamical systems?
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Recent advances in bifurcation analysis and numerical methods for modeling complex dynamical systems include the utilization of tools like DDE-BIFTOOL for studying delay differential equations (DDEs) with state-dependent delays . Additionally, a novel approach using equation-driven neural networks (EDNNs) has been developed to compute bifurcations in nonlinear parametric systems, demonstrating feasibility through theoretical convergence analysis and numerical implementation . MatCont, a toolbox based on bifurcation theory, enables the computation of bifurcation diagrams through numerical continuation, allowing for the detection and continuation of new bifurcations in both continuous and discrete-time systems . These advancements provide valuable insights into the solution structures, stability, and qualitative changes of complex dynamical systems under varying parameters.
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| Papers (5) | Insight |
|---|---|
| Recent advances in bifurcation analysis include MatCont's innovations in detecting and continuing new bifurcations in discrete-time systems through numerical methods, enhancing the understanding of complex dynamical systems. | |
Open access•Journal Article | Recent advances include utilizing tools from bifurcation theory, like DDE-BIFTOOL, for studying systems with delays, analyzing steady states, periodic orbits, codimension one bifurcations, and detecting codimension two bifurcations. |
| Recent advances include utilizing equation-driven neural networks for bifurcation analysis in nonlinear parametric systems, offering a novel approach combining machine learning and numerical methods for modeling complex dynamical systems. | |
| Recent advances include utilizing tools like DDE-BIFTOOL for studying systems with delays, analyzing steady states, periodic orbits, and bifurcations of various codimensions in applications like El Niño modeling. | |
| Recent advances include new results in differential-algebraic systems, advanced numerical methods, chaotic dynamics, slow-fast systems, global bifurcations, invariant manifolds, and applications in neuroscience, ecology, and engineering. |
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