Most of the formalisms of fuzzy cognitive maps (FCM) that had been proposed and applied in the past are relatively simple in the sense that they handle the various interacting and time-varying concepts as zeroth-order dynamical components. That is, they do not accommodate time delays and growth exponential time constants. In modeling real life systems, especially in the general domain of socio-politico-economics, the time delays are often important and need to be accounted. Also, the various sensitivities associating the system concepts may be time dependent. In the present work, a previously proposed FCM has been extended to include time delays, time constants and time-dependent sensitivities. The system has been applied to the Cyprus politico-economic dynamics, with emphasis on possible scenarios involving the finding and exploitation of oil/gas in the exclusive economic zone of Cyprus. The existence of natural gas - estimated at about 7 trillion cubic feet - has recently been preliminarily verified. In the interrelated dynamics, various important dynamical parameters have been taken into account, reflecting the interests of primarily the republic of Cyprus, as well as the interests of the Greek and Turkish Cypriot communities and other countries involved, such as Greece, Turkey, United Kingdom, USA, Russia, Israel and the European Union. The main parameters that had been considered in the interrelated dynamics are nationalism, religiousness, unemployment, external debt, oil extraction and the general interests of the countries involved and those of the two communities.