PERIOD-ADDING IN A THREE-DIMENSIONAL DYNAMICAL SYSTEM
PAULO C. RECH *
Departamento de Fsica, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil
*Author to whom correspondence should be addressed.
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.
Keywords: Parameter plane, largest lyapunov exponent, period-adding, chaos, periodicity