Growth dynamics of domain pattern in a three-trophic population model

Lee, S.-H.; Pak, Hyuk Kyu; Wi, Haeng Sub; Chon, Tae‐Soo; Matsumoto, Takashi

doi:10.1016/j.physa.2003.11.017

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…First, the different scales of the animal body; for example, Waliszewski et al reported that the microscopic gene expression and the macroscopic cellular proliferation were scale-invariant systems [ 25 ], the scale-free feature of which was shown to result in the emergence of organizational dynamics at all hierarchical levels of the living matter [ 26 ]. Secondly, metazoan cells develop from a single cell, and this involves complex spatio-temporal events [ 11 , 27 ].…”

Section: Introductionmentioning

confidence: 99%

Self-organization of developing embryo using scale-invariant approach

Tiraihi

2011

Theor Biol Med Model

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BackgroundSelf-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.MethodsIn this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.Results and conclusionThe fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.

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Section: Introductionmentioning

confidence: 99%

Self-organization of developing embryo using scale-invariant approach

Tiraihi

2011

Theor Biol Med Model

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“…Modeling of food chain dynamics has challenges in the fields of both theoretical ecology and applied mathematics. Tri-trophic food chain models have been studied in both spatially homogeneous [1][2][3][4] and spatially inhomogeneous environments [5][6][7][8][9][10] for the last two decades. Those models exhibit rich and complex dynamics and nonlinear mathematical behavior, including varying numbers and stability of equilibrium states, limit cycles, patterns and chaos.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

Melese¹,

Gakkhar²

2011

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In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripelike patterns.

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Effects of the probability of a predator catching prey on predator–prey system stability

Lee

2011

Journal of Asia-Pacific Entomology

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Growth dynamics of domain pattern in a three-trophic population model

Cited by 4 publications

References 19 publications

Self-organization of developing embryo using scale-invariant approach

Self-organization of developing embryo using scale-invariant approach

Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

Effects of the probability of a predator catching prey on predator–prey system stability

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