May–Wigner stability theorem
E548444
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in random matrix theory ⓘ result in theoretical ecology ⓘ |
| analyzes | real parts of eigenvalues of the community matrix ⓘ |
| appliesTo |
ecological communities
ⓘ
large dynamical systems ⓘ |
| assumes |
entries of the interaction matrix are independent random variables with zero mean
ⓘ
large system size ⓘ linearization around an equilibrium ⓘ random interactions between components ⓘ |
| concerns |
local stability of equilibria
ⓘ
random interaction matrices ⓘ stability of large complex systems ⓘ |
| field |
complex systems theory
ⓘ
random matrix theory ⓘ theoretical ecology ⓘ |
| givesCondition |
S·C·σ < 1 for all eigenvalues to have negative real part in a common variant
ⓘ
S·C·σ² < 1 for local stability in May’s original formulation ⓘ |
| hasConsequence |
challenges the idea that complexity always promotes stability
ⓘ
motivated research on structured interaction networks ⓘ motivated study of non‑random interaction patterns in ecology ⓘ |
| hasParameter |
connectance C
ⓘ
number of species S ⓘ standard deviation of interaction strengths σ ⓘ |
| implies | increasing complexity tends to reduce stability ⓘ |
| influencedField |
ecological network theory
ⓘ
engineering of complex networks ⓘ systems biology ⓘ |
| inspiredBy |
Wigner’s semicircle law
NERFINISHED
ⓘ
Wigner’s work on random matrices in nuclear physics ⓘ |
| introducedBy | Robert M. May NERFINISHED ⓘ |
| namedAfter |
Eugene Wigner
NERFINISHED
ⓘ
Robert May NERFINISHED ⓘ |
| originalContext | stability and complexity in model ecosystems ⓘ |
| predicts |
critical complexity threshold for stability
ⓘ
loss of stability when complexity exceeds a critical value ⓘ |
| publicationYear | 1972 ⓘ |
| publishedIn | Nature NERFINISHED ⓘ |
| relates |
stability to connectance
ⓘ
stability to interaction strength ⓘ stability to system size ⓘ |
| stabilityCriterion | all eigenvalues must have negative real parts for local stability ⓘ |
| states | large complex systems with sufficiently strong random interactions are generically unstable ⓘ |
| typeOf | linear stability result ⓘ |
| usesConcept |
Jacobian matrix
NERFINISHED
ⓘ
circular law ⓘ community matrix ⓘ eigenvalue spectrum ⓘ random matrices with independent entries ⓘ |
Referenced by (1)
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