In this work, we consider a complex network of predator-prey systems, modeling the ecological dynamics of interacting species living in a fragmented environment. We consider non-identical instances of a Lotka-Volterra model with Holling type II functional response. We study optimal control problems, for the minimization of the default of synchronization in the complex network, where the controls reproduce the implementation of ecological corridors. The main goal is to restore biodiversity of life species in a heterogeneous habitat by reaching at least a global coexistence equilibrium, or in a better scenario, a global limit cycle which would guarantee biological oscillations, which means rich life dynamics.

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