We analyse the use of parametric and quasiperiodic modulations in suppressing horseshoe structure in the phase plane of perturbed pendulum systems. Taking the Froude pendulum as a typical system, four different modulation mechanisms are studied by deriving analytic expressions for the window of the strength of modulation giving suppression in each case. A comparison of the four cases from the point of view of flexibility and efficiency is also given.

We report the formation of Cantor set-like fractals during the development of coherent structures in a coupled map lattice (CML). The dependence of these structures on the size of the lattice as well as the first three dimensions of the associated fractal patterns are analyzed numerically.

We present the results of extensive numerical studies on stochastic resonance and its characteristic features in three model systems, namely, a model for Josephson tunnel junctions, the bistable cubic map and a coupled map lattice formed by coupling the cubic maps. Some interesting features regarding the mechanism including multisignal amplification and spatial stochastic resonance are shown.

The correlation dimension $D_{2}$ and correlation entropy $K_{2}$ are both important quantifiers in nonlinear time series analysis. However, use of $D_{2}$ has been more common compared to $K_{2}$ as a discriminating measure. One reason for this is that $D_{2}$ is a static measure and can be easily evaluated from a time series. However, in many cases, especially those involving coloured noise, $K_{2}$ is regarded as a more useful measure. Here we present an efficient algorithmic scheme to compute $K_{2}$ directly from a time series data and show that $K_{2}$ can be used as a more effective measure compared to $D_{2}$ for analysing practical time series involving coloured noise.

We present a mechanism for the synchronization of one-way coupled nonlinear systems in which the coupling uses a variable delay, that is reset at finite intervals. Here the delay varies in the same way as the system in time and so the coupling function remains constant for the reset interval at the end of which it is reset to the value at that time. This leads to a novel and discrete error dynamics and the resulting general stability analysis is applicable to chaotic or hyperchaotic systems. We apply this method to standard chaotic systems and hyperchaotic time delay systems. The results of the detailed numerical analysis agree with the results from stability analysis in both cases. This method has the advantage that it is cost-effective since information from the driving system is needed only at intervals of reset. Further, in the context of time delay systems, optimization among the different time-scales depending upon the application is possible due to the flexibility among the four different time-scales in our method, viz. delay in the driving system, anticipation in the response system, system delay time and reset time. We suggest a bi-channel scheme for implementing this method in communication field with enhanced security