Universal Bifurcation Chaos Theory and Its New Applications

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems ordinary partial differential equations, which are models autocatalytic chemical processes interacting populations, is carried out. It shown analytically numerically that all considered further complication dynamics solutions biological turbulence out full accordance with universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic homoclinic cascades bifurcations stable limit cycles. case, irregular (chaotic) attractors cases exclusively singular sense FShM theory. The obtained results once again indicate wide applicability for describing laminar–turbulent transitions chaotic complex equations system can be confirmed only by detection some main cycles or tori diagram presented article.