P systems with energy accounting

We consider P systems where each evolution rule "produces" or "consumes" so me quantity of energy, in amounts which are expressed as integer numbers. I n each moment and in each membrane the total energy involved in an evolutio n step should be positive, but if "too much" energy is present in a membran e, then the membrane will be destroyed (dissolved). We show that this featu re is rather powerful. In the case of multisets of symbol-objects we find t hat systems with two membranes and arbitrary energy associated with rules, or with arbitrarily many membranes and a bounded energy associated with rul es, characterize the recursively enumerable sets of vectors of natural numb ers (catalysts and priorities are used). In the case of string-objects we h ave only proved that the recursively enumerable languages can be generated by systems with arbitrarily many membranes and bounded energy; when boundin g the number of membranes and leaving free the quantity of energy associate d with each rule we have only generated all matrix languages. Several resea rch topics are also pointed out.