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Antagonistic interactions (predation) between two quantifiable entities (populations for example) lead to evolutionary processes that often show stable periodic cycles (attractors) exhibiting perfectly identifiable phases (excess, collapse, resilience). In more complex cases of interaction where predators also have a beneficial collateral influence on prey, there may be an initial phase of mutual development of the two populations. These phenomena are triggered when the efficiency of the predation mechanism is high enough. We describe these behaviors in the frameworks of both biology and economics.