Parameter-robustness analysis for a biochemical oscillator model describing the social-behaviour transition phase of myxobacteria (original) (raw)
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We analyze a mathematical model of a simple microbial system consisting of two microbial populations competing for a single nutrient and two predator populations, each one feeding upon one competitor, in a chemostat. Monod's model is employed for the specific growth rates of all the microbial populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. We demonstrate that the system exhibits chaotic behavior and multistability. Two different routes to chaos are observed. Chaotic behavior is reached either through a sequence of period doublings or through birth and breaking of quasi-periodic states, as the operating conditions are varied. In some cases, transition from periodic to chaotic behavior is accompanied at certain parameter values by limit-point bifurcations of periodic states, the effect being multistablity, i.e. coexistence of stable periodic states with other stable periodic, quasi-periodic or chaotic states. The results demonstrate the importance of the interaction of food chains with regard to the dynamics exhibited by systems of microbial species inhabiting a common environment.
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Bulletin of Mathematical Biology, 1992
The forced double-Monod model (for a chemostat with a predator, a prey and periodically forced inflowing substrate) displays quasiperiodicity, phase locking, period doubling and chaotic dynamics. Stroboscopic sections reveal circle maps for the quasiperiodic regimes and noninvertible maps of the interval for the chaotic regimes. Criticality in the circle maps sets the stage for chaos in the model. This criticality may arise with an increase in the period or amplitude of forcing.
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Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually, or if they can emerge instantly with a non-zero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a non-oscillating attractor coexist in phase space. We experimentally validate this prediction by...
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Discrete & Continuous Dynamical Systems - B, 2020
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