For over a decade, the multi-agent patrolling task has received attention from the multi-agent community. A range of algorithms based on reactive and cognitive architectures has been developed. However, the existing patrolling specific approaches regarding dynamic environment are still in preliminary stages. In this paper, we present a first study opening the multi-agent patrolling task to the assumption of varying environment. In order to accomplish this study we propose a formal model for dynamic environment grounded on the one hand on classical patrolling model and on the other hand on edge-Markovian evolving graphs. An adaptation of two very different strategies of agent, Conscientious Reactive and Heuristic Pathfinder Cognitive Coordinated, to that environment is designed, implemented in a simulator and assessed. The results, show the architecture implementing Heuristic Pathfinder Cognitive Coordinated strategy can patrol an area into dynamic environment more adequately than the one implementing the Conscientious Reactive strategy. Moreover the difference between the two strategies is larger in dynamic environment than in static environment.