Explaining the Bifurcation Diagram using Local Maxima

An instructional video on what the bifurcation diagram represents, and how to plot it. The Rossler chaotic system is used as an example, being one of the most well known chaotic systems. The video is based on the following paper: Moysis, L., Lawnik, M., Fragulis, G. F., & Volos, C. (2025). Continuous-Time Density-Colored Bifurcation Diagrams. International Journal of Bifurcation and Chaos, 2530028. https://www.worldscientific.com/doi/abs/10.1142/S0218127425300289 https://www.researchgate.net/publication/394842432_Continuous-Time_Density-Colored_Bifurcation_Diagrams Matlab code: https://uk.mathworks.com/matlabcentral/fileexchange/181870-continuous-time-density-colored-bifurcation-diagrams?s_tid=srchtitle https://www.youtube.com/watch?v=p9mg6TOBMY0 Full playlist: https://www.youtube.com/playlist?list=PL9y6bivP9mhEojwAXJ2R85cK5XhedDHOr Chaos theory studies how small changes in initial conditions can lead to vastly different outcomes in certain systems, making long-term prediction nearly impossible. It’s often illustrated by the “butterfly effect,” where something as tiny as a butterfly flapping its wings could, in theory, influence weather patterns weeks later. Despite appearing random, chaotic systems follow underlying deterministic rules—they’re just incredibly sensitive, so their complexity hides their order. Social: https://www.linkedin.com/in/moysislazaros/ https://www.researchgate.net/profile/Lazaros-Moysis #chaos #chaostheory #nonlinear #attractor #strangeattractor #nonlineardynamics #rossler #bifurcation #physics #stem #mathematics #matlab #butterflyeffect #differentialequation #dynamics #dynamicalsystems #differentialequation #differentialequations #ode #physicseducation #mathematicseducation #poincare #plane #equilibria #periodicity #entropy #modeling #physicalmodeling #chaotic #maths #engineering #science #research #academia #signalprocessing