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Equilibrium in a large Lotka–Volterra system with pairwise correlated interactions

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  • Clenet, Maxime
  • El Ferchichi, Hafedh
  • Najim, Jamal

Abstract

Consider a Lotka–Volterra (LV) system of coupled differential equations: ẋk=xk(rk−xk+(Bx)k),x=(xk),1≤k≤n,where r=(rk) is a n×1 vector and B a n×n matrix. Assume that the interaction matrix B is random and follows the elliptic model: B=1αnA+μn1n1nT,where A=(Aij) is a n×n matrix with N(0,1) entries satisfying the following dependence structure (i) the entries Aij on and above the diagonal are i.i.d., (ii) for i

Suggested Citation

  • Clenet, Maxime & El Ferchichi, Hafedh & Najim, Jamal, 2022. "Equilibrium in a large Lotka–Volterra system with pairwise correlated interactions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 423-444.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:423-444
    DOI: 10.1016/j.spa.2022.08.004
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    1. Jacopo Grilli & Matteo Adorisio & Samir Suweis & György Barabás & Jayanth R. Banavar & Stefano Allesina & Amos Maritan, 2017. "Feasibility and coexistence of large ecological communities," Nature Communications, Nature, vol. 8(1), pages 1-8, April.
    2. Stefano Allesina & Si Tang, 2012. "Stability criteria for complex ecosystems," Nature, Nature, vol. 483(7388), pages 205-208, March.
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