From integrability to chaos in a Lotka-Volterra cellular automaton

Hirota, Ryogo; Iwao, Masataka; Ramani, A.; Takahashi, Daisuke; Grammaticos, B.; Ohta, Yuichi

doi:10.1016/s0375-9601(97)00721-4

Cited by 20 publications

(10 citation statements)

References 23 publications

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“…The overall behaviour such as single species extinction, both species extinction and coexistence are examined first. Following that, stationarity (Azar et al 1995) and chaotic dynamics (Hirota et al 1997) are analyzed by using the procedure for screening time Figure 4 | Snapshot of population dynamics at t ¼ 1,050 (left); predator population dynamics and harvest (right). Simulation results of the updated EcoCA model; the square grid is 20 £ 20; initial condition is prey ¼ 100 and predator ¼ 100; neighbourhood is Moore scheme; jointly harvesting of prey and predator at the same constant effort 15%; harvesting criterion is 10%.…”

Section: Simulation Of Harvest Strategiesmentioning

confidence: 99%

Cellular-automata-based ecological and ecohydraulics modelling

Chen

2009

Journal of Hydroinformatics

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Spatially lumped models may fail to take into account the effects of spatial heterogeneity and local interactions. These properties sometimes are crucial to the dynamics and evolutions of ecosystems. This paper started from the fundamental aspects of CA and focused on the development and application of the approach to ecological and ecohydraulics modelling.Application cases include modelling of prey-predator dynamics by stochastic CA and simulation of riparian vegetation successions in a regulated river by rule-based CA. The results indicated that spatially explicit paradigms such as cellular automata (CA) have a strong capability to bridge the local processes and global patterns.

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Section: Simulation Of Harvest Strategiesmentioning

confidence: 99%

Cellular-automata-based ecological and ecohydraulics modelling

Chen

2009

Journal of Hydroinformatics

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“…(14) are given by eq.(15). The purpose of this subsection is to write them explicitly in the case of NSRM.…”

Section: Rational Mapsmentioning

confidence: 99%

“…2 corresponds to the case of A 1 + A 2 + A 3 = 0 and j = 0. The straight lines in these figures are known to correspond to integrable orbits [14]. Figures 3 and 4 are the cases of j = 1 and j = 2 respectively.…”

Section: Numerical Observation Of Ultra-discrete Version Of the Atypementioning

confidence: 99%

Möbius Symmetry of Discrete Time Soliton Equations

Yamamoto

2003

J. Phys. Soc. Jpn.

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“…Introduction. The non-analytic limit [1,3] lim →+0 log exp U + exp V + · · · + exp W = max(U, V, . .…”

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confidence: 99%

“…. , W ) (1) has been introduced into soliton theory and used to translate many fully discrete soliton equations into the corresponding soliton cellular automaton [2,4]. Nowadays, formula (1) is called the ultradiscrete limit, since the soliton equation of fully discrete independent variables is further transformed through this limit into a system whose dependent variables are also discretized.…”

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confidence: 99%