Simple mathematical models with very complicated dynamics

By R. May. 1976

Subfields: Network Science & Complex Systems

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Citations in the corpus

The large learning rate phase of deep learning: the catapult mechanism (2020, background): “We point to the logistic map (May, 1976) as a well-known example of a dynamical system that undergoes phase transitions as a function of an external parameter.”
A lower bound error for free-run simulation of the polynomial NARMAX (2016, methodology): “(1987) used computational effort to prove a theorem which states that a pseudo-orbit of the logistic map (May, 1976) remains at a distance of 10−7 from the true orbit up to 10 million iterations using double”
Predicting potential distributions of invasive species: where to go from here? (2010, unknown): “model) (May, 1976) Parameterization of dispersal”
Improved particle swarm optimization combined with chaos (2005, methodology): “In this paper, the well-known logistic equation [15], which exhibits the sensitive dependence on initial conditions, is employed for constructing hybrid PSO.”
Multifractals: Theory and Applications (2001, background): “These may be suggestive of the required conditions in more general situations. When Does F (y) = e F (y)? The following results are special cases of those in Cawley & Mauldin (1992) applied to the multinomial measures of Example 4.”
The state of plant population modelling in light of environmental change (2008, background): “Some of the more recent developments have included an increasing scepticism regarding equilibrium approaches, starting in the 1970s and 1980s (Reddingius, 1971; May, 1976), the implicit and more recent explicit inclusion of spatial components in demographic modelling (e.”
Algebraically Simple Chaotic Flows (2000, background): “Note that the scales are plotted backwards to emphasise the similarity to the logistic map, xn+1 = Axn(1 – xn) [24].”
Chaos-enhanced accelerated particle swarm optimization (2013, background): “The iterative chaotic map with infinite collapses [23] is expressed by:”
The dynamics of collapse in world fisheries (2005, background): “Since the seminal paper of May (1976), irregular solutions (such as those of erratic collapses) to dynamical systems, in contrast with regular solutions (such as those of smooth collapses and plateau-shaped collapses), can be interpreted within the framework of the chaos theory.”
Spatial-temporal population dynamics across species range: from centre to margin (2005, background): “Most previous theoretical and empirical studies on population dynamics focused only on the temporal patterns of local populations (May 1976), with little attention paid to the differences in birth and death rates in different habitats and migration rates across habitats within the species’ range…”