  Recently a method which employs computing of fluctuations in a measure of
nonlinear similarity based on local recurrence properties in a univariate time
series, was introduced to identify distinct dynamical regimes and transitions
between them in a short time series [1]. Here we present the details of the
analytical relationships between the newly introduced measure and the well
known concepts of attractor dimensions and Lyapunov exponents. We show that the
new measure has linear dependence on the effective dimension of the attractor
and it measures the variations in the sum of the Lyapunov spectrum. To
illustrate the practical usefulness of the method, we employ it to identify
various types of dynamical transitions in different nonlinear models. Also, we
present testbed examples for the new method's robustness against the presence
of noise and missing values in the time series. Furthermore, we use this method
to analyze time series from the field of social dynamics, where we present an
analysis of the US crime record's time series from the year 1975 to 1993. Using
this method, we have found that dynamical complexity in robberies was
influenced by the unemployment rate till late 1980's. We have also observed a
dynamical transition in homicide and robbery rates in the late 1980's and early
1990's, leading to increase in the dynamical complexity of these rates.
