... of fixed points is discussed and illustrated through cobweb diagrams. We deal with quantitative universality, such as orbit diagrams and Lyapunov exponents for a class of rational maps. We show that our model is periodic using orbit diagrams and relevant Lyapunov exponents. e-mails:  hakin@ictp.it...

...Changpin Li; Chuntao Yin This paper is devoted to estimating the bound of the Lyapunov exponents for the Caputo–Hadamard fractional differential system. First, using the Gronwall inequality, we analyze the continuous dependence of the solution to the Caputo–Hadamard fractional initial value problem...

... equations of mechanism with clearance joints. Lyapunov exponent is used to analyze the motion status, chaotic or periodic, of the slider. Based on data points, mean absolute deviation (MAD) is applied to judge the dynamical errors, displacement, velocity, and acceleration, of the slider due to clearance...

..., including chaotic vibrations, appear after the Hopf bifurcation when the excitation frequency decreases. Lyapunov exponents are numerically calculated to prove the occurrence of chaotic vibrations. Bifurcation sets are also calculated to investigate the influence of the system parameters on the response...

... Lyapunov exponent in numerically assessing the responses of nonlinear dynamic systems is presented. As the overlapping points of the k th group among the the j groups of overlapping points may not necessarily be periodic points, distinguishing periodic points from the other nonperiodic...