PERIOD-ADDING IN A THREE-DIMENSIONAL DYNAMICAL SYSTEM

This paper reports on parameter plane diagrams numerically obtained for a particular threedimensional, four-parameter, continuous-time mathematical model. The dynamical behavior is characterized by considering the largest Lyapunov exponent as an indicator of chaos or periodicity. All of the six pairs of parameters are investigated. It is shown that, whatever the combination of parameters considered, an interesting scenario is always preserved, namely one in which the parameter plane displays typical periodic structures embedded in a chaotic region. It is also shown that there are some type of organization of these periodic structures, in period-adding bifurcation cascades.