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We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a nontrivial invariant measure for this case.doi:10.1214/105051607000000203 fatcat:sxzqxltjwbdxropat3evyc2zwy