Interested in analyzing delay differential equations? This paper introduces DDE-BIFTOOL, a powerful Matlab package designed for numerical bifurcation analysis of systems involving delay differential equations with multiple fixed, discrete delays. This tool is a boon for researchers working with complex dynamic systems. The study details the package's capabilities, which include the continuation of steady-state solutions and periodic solutions, along with stability analysis. It also allows the computation and continuation of steady-state fold and Hopf bifurcations, enabling users to switch to the emanating branch of periodic solutions. Through analyzing models of coupled neurons with delayed feedback and coupled oscillators with delay, the paper highlights the package's versatility and utility. DDE-BIFTOOL provides a robust and user-friendly environment for exploring the dynamics of systems governed by delay differential equations, making it a valuable asset for researchers across various scientific disciplines.
As a publication in ACM Transactions on Mathematical Software, this paper fits squarely within the journal's scope of disseminating high-quality, well-documented, and tested mathematical software. The description of DDE-BIFTOOL, its underlying numerical methods, and illustrative examples directly serve the journal's objective of advancing computational tools for the mathematical and scientific community. The references included highlight the software's foundations and related research.