A model of two consumer-resource systems linked by interspecific interference
competition of consumers is considered. The basic assumption of the model is
that the dynamics of the resource is much slower than that of the consumer. In
the absence of interaction each consumer-resource pair has a unique stable
steady state which is completely nonoscillatory. When weakly coupled, the
consumer-resource pairs are shown to exhibit sustained low-frequency
synchronous antiphase relaxation oscillations.Comment: 24 pages, 4 figures, 1 table, 38 references. Postprint of the
published article. arXiv admin note: substantial text overlap with
arXiv:1409.440
Cell-cycle synchronization of two diffuse-coupled cells has been studied in the framework of the membrane model for the cell division cycle, proposed by Chernavskii et al. (1977). It has been shown semi-analytically (using the averaging principle) and by computer stimulation that a) if the duration of the G1-phase (TG1) for two identical cells is comparable with the duration of the remaining cycle (TS + G2 + M), the lipid (L)-exchange results in a synchronization with phase difference phi = 0. The antioxidant (A)-exchange leads to a phase-locking with phi = T0/2 (where T0 is the cell cycle period; b) if TG1 much greater than TS + G2 + M (or TG1 much less than TS + G2 + M) the L-exchange makes synchronization possible both with phi = 0 and phi = T0/2 while the A-exchange results in phase-locking with phi confined to the region 0 to T0/2; c) for non-identical cells differing in the values of kinetic parameters, the locking band narrows as the population density increases (when some model parameters are close to the bifurcation thresholds). We expect that the cells selected artificially at a definite phase of cycle might maintain the synchronous division for a long time if the lipid exchange between cells were stimulated.
Self-sustained antiphase relaxation oscillations of high amplitude are shown
to be possible in a system of two single-mode semiconductor lasers strongly
coupled through their cavities.Comment: 10 pages, 6 figures, 1 tabl
The work develops and investigates a mathematical model for evolution of the technological structure of an economic system where different technologies compete for the common essential resources. The model is represented by a system of consumer–resource rate equations. Consumers are technologies formalized as populations of weakly differentiated firms producing a similar commodity with like average output. Firms are characterized by the Leontief–Liebig production function in stock-flow representation. Firms self-replicate with a rate proportional to production output of the respective technology and dissolve with a constant rate of decay. The resources are supplied to the system from outside and consumed by concerned technologies; the unutilized resource amounts are removed elsewhere. The inverse of a per firm break-even resource availability is proposed to serve as a measure for competitiveness towards a given resource. The necessary conditions for coexistence of different technologies are derived, according to which each contender must be a superior competitor for one specific resource and an inferior competitor for the others. The model yields a version of the principle of competitive exclusion: in a steady state, the number of competing technologies cannot exceed the number of limiting resources. Competitive outcomes (either dominance or coexistence) in the general system of multiple technologies feeding on multiple essential resources are shown to be predictable from knowledge of the resource-dependent consumption and growth rates of each technological population taken alone. The proposed model of exploitative competition with explicit resource dynamics enables more profound insight into the patterns of technological change as opposed to conventional mainstream models of innovation diffusion.
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