Applied Mathematics & Information Sciences

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This paper deals with the derivation of hyperbolic equations from a space inhomogeneous thermostatted kinetic equation which can be proposed for the modeling of complex systems subjected to the external actions at the microscopic and macroscopic scales. The particles of the system are able to perform an activity which is modeled by introducing a specific variable. The derivation of the hyperbolic equations is obtained by performing different scalings into the time and space variables and letting the scaling parameter goes to zero. Applications and future research direction are discussed into the last section of the paper.