Synchronisation of chaotic metapopulations in a cascade of coupled logistic map models

The dynamics of metapopulations in two patches undergoing migration among each other has commonly been analysed by using two coupled logistic map models. Considering two sets of such coupled patches which are all exhibiting chaotic oscillations, it is shown here that the chaotic metapopulations of the second set of patches (response system) can be synchronised with that of the first set of patches (drive system) by using a simple synchronisation technique which requires a selective migration only from the drive system patches. After synchronisation, the populations of the response system patches exhibit chaotic oscillations which are exactly similar to that of the drive system patches, irrespective of their initial population sizes. It has also been shown that cascading of many such response system patches, in a similar way, results in synchronisation of the chaotic metapopulations in all of them. Finally, it is observed that slight inhomogeneities in the environment affects the suggested synchronisation procedure which can be regained by the addition of small external noise to the system.