Simple mathematical models with very complicated dynamics¶
May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459-467.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Chaos
- the attractor is the climate regime (Lorenz attractor in the canonical reduction). Biology and ecology → the rule is the population dynamics (logistic, Lotka-Volterra, neural-firing equations); the state space is population-size or membrane-voltage space; sensitive dependence appears in high-reproduction populations
This sourceSeminal paper showing that the logistic recurrence x_{n+1}=r·x_n·(1−x_n) generates fixed points, period-doubling cascades, and chaos depending on r; demonstrates substrate-independent recurrence across ecology, economics, and physics.
Supported in partVerified against the publisher's abstract
May 1976's abstract backs only the biology/ecology frame: simple deterministic first-order difference equations in the biological sciences can produce stable points, bifurcating cycles and apparently random fluctuations.
“First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.”
- the attractor is the climate regime (Lorenz attractor in the canonical reduction). Biology and ecology → the rule is the population dynamics (logistic, Lotka-Volterra, neural-firing equations); the state space is population-size or membrane-voltage space; sensitive dependence appears in high-reproduction populations
- Nonlinearity
- Qualitative phenomena enabled: a stable equilibrium at `N = K`, monotone approach from any positive initial condition, and — when the same logic is extended to discrete time as the logistic map* `x_{n+1} = rx_n(1 − x_n)` — a period-doubling cascade leading to chaos for `r > 3.57…` (May 1976
This sourceSeminal paper showing that the logistic recurrence x_{n+1} = r·x_n·(1−x_n) generates fixed points, period-doubling cascades, and chaos depending on r, demonstrating substrate-independent recurrence behavior across ecology, economics, and physics.
- Qualitative phenomena enabled: a stable equilibrium at `N = K`, monotone approach from any positive initial condition, and — when the same logic is extended to discrete time as the logistic map* `x_{n+1} = rx_n(1 − x_n)` — a period-doubling cascade leading to chaos for `r > 3.57…` (May 1976
- Recurrence
- The structural insight is robust: a Fibonacci population doubling, a sunspot cycle, an empire's rise-and-fall, neural signal propagation in feedback loops, and a chronic relapse cycle all exhibit the same recurrence logic: current state encodes history and influences futures—a unifying point May (1976) made starkly when he showed that the same one-line recurrence relation produces fixed points, oscillations, and chaos across ecology, economics, and physiology.
This sourceSeminal paper showing that the logistic recurrence x_{n+1} = r·x_n·(1−x_n) generates fixed points, period-doubling cascades, and chaos depending on r, demonstrating substrate-independent recurrence behavior across ecology, economics, and physics.
Supported in partVerified against the publisher's abstract
Abstract supports first-order equations yielding stable points, cycles, and random fluctuations in biological/economic/social contexts, but not the claim's specific examples or physiology.
“First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.”
- The structural insight is robust: a Fibonacci population doubling, a sunspot cycle, an empire's rise-and-fall, neural signal propagation in feedback loops, and a chronic relapse cycle all exhibit the same recurrence logic: current state encodes history and influences futures—a unifying point May (1976) made starkly when he showed that the same one-line recurrence relation produces fixed points, oscillations, and chaos across ecology, economics, and physiology.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 2 of 3 citations: 2 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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