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Title:
A Nonlinear Analogue of May-Wigner Instability Transition
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Abstract:
The prevailing view in the mid-twentieth century was that diverse ecosystems have more resilience to recover from events displacing the system from equilibrium and hence are more stable. This `ecological intuition' was challenged by Robert May in 1972 in his article in Nature where he considered a model ecosystem of N species at an equilibrium subject to random linear interaction between them. Invoking properties of large random matrices due to Wigner, May concluded that the system will almost certainly become unstable as N becomes larger and larger.
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