Bifurcation phenomena of the non-associative octonionic quadratic

In this work we have performed an investigation into the limiting dynamics and bifurcation phenomena of the non-associative octonionic quadratic map. It displayed a wealth of nonlinear structure including fixed points, Hopf bifurcations, phase locking, periodic cycles, tori, nontrivial knots, loop doubling and tripling, infinite period doubling cascades and hyperchaos. The evolution of the limiting structure was characterized by the recursive interplay of these various bifurcation mechanisms, which led to the appearance of complex attracting structures. Connections from this behaviour to the theory of the Mandelbrot set were established.