Variation of certain statistical quantities near critical bifurcations

We study the behaviour of average value of state variable X and maximal Lyapunov exponent at various bifurcations of chaos in logistic map and Bonhoeffer–van der Pol (BVP) equation. Power-law variation is observed near sudden widening and intermittency bifurcations while linear variation is found near band-merging bifurcation. The fluctuation of a coarse-grained coordinate ξn near the critical bifurcations is characterized using its variance σn(q),−∞