On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π‐criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation‐optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash‐out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square‐wave forcing leads in practice to the extinction of the wash‐out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Cycles in cannibalistic egg-larval interactions

A model of a cannibalistic larval-egg interaction such as occurs in Tribolium is developed which leads to a system of nonlinear Volterra integral equations. I determine the local stability properties of the unique equilibrium point of the model. A Hopf bifurcation analysis shows that the model always undergoes a subcritical bifurcation when stability is lost. Numerical solutions confirm the presence of multiple attractors over a range of parameter values. The form of the cycles observed in the numerical solutions is analogous to that observed in laboratory populations of Tribolium.     

Oscillations in a system with material cycling

We study a system of two integrodifierential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By Hopf bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.Work performed within the activity of the research group Evolution Equations and Physico-Mathematical Applications, M.P.I. (Italy), and under the auspices of G.N.F.M., C.N.R. (Italy)     

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one.     

Some epidemiological models with nonlinear incidence

Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.Research supported in part by Centers for Disease Control Contract 200-87-0515. Support services provided at University House Research Center at the University of IowaResearch supported in part by NSERC A-8965 and the University of Victoria President's Committee on Faculty Research and Travel     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

Global bifurcations in the FitzHugh-Nagumo equations for nerve wave propagation

The FitzHugh-Nagumo equations for action potential propagation along nerve axons and the corresponding ordinary differential equations for travelling waves are solved numerically. Above a critical value, a constant bias current can drive a wave-front solution. At the critical value, a global bifurcation occurs. As a result, the wave front switches into a pulse.Based on a thesis by one of the authors (H. F.).     

Odor preference in honeybees as a function of amount of reward: Tests of two explanations

How does a foraging honeybee come to prefer a color or odor paired with the large of two amounts of sucrose solution to a color or odor paired with the smaller amount? One hypothesis is that the attractiveness of a color or odor is based on the strength of its association with the taste of sucrose, which increases with the duration of concurrent color-taste or odor-taste stimulation. Another hypothesis is that the attractiveness of a color or odor is based on association with the afferent consequences of feeding, which are different for the two amounts. Both hypotheses were tested in experiments on proboscis-extension conditioning, a technique that provides better control of stimulation than is possible in work with free-flying foragers. In Experiments 1–3, which were designed to test the first hypothesis, an odor that accompanied the ingestion of sucrose on training trials was found to elicit extension of the proboscis when subsequently it was presented alone, but the duration of concurrent stimulation had no significant effect on the probability or persistence of the response. In Experiments 4 and 5, which were designed to test the second hypothesis, an odor that immediately followed the ingestion of sucrose on training trials failed to elicit extension of the proboscis when subsequently it was presented alone. The results support neither hypothesis.     

Spontaneous allelic variant in deafness–blindness gene Ush1g resulting in an expanded phenotype

Relationships between novel phenotypic behaviors and specific genetic alterations are often discovered using target-specific, directed mutagenesis or phenotypic selection following chemical mutagenesis. An alternative approach is to exploit deficiencies in DNA repair pathways that maintain genetic integrity in response to spontaneously induced damage. Mice deficient in the DNA glycosylase NEIL1 show elevated spontaneous mutations, which arise from translesion DNA synthesis past oxidatively induced base damage. Several litters of Neil1 knockout mice included animals that were distinguished by their backwards-walking behavior in open-field environments, while maintaining frantic forward movements in their home cage environment. Other phenotypic manifestations included swim test failures, head tilting and circling. Mapping of the mutation that conferred these behaviors showed the introduction of a stop codon at amino acid 4 of the Ush1g gene. Ush1g^bw/bw null mice displayed auditory and vestibular defects that are commonly seen with mutations affecting inner-ear hair-cell function, including a complete lack of auditory brainstem responses and vestibular-evoked potentials. As in other Usher syndrome type I mutant mouse lines, hair cell phenotypes included disorganized and split hair bundles, as well as altered distribution of proteins for stereocilia that localize to the tips of row 1 or row 2. Disruption to the bundle and kinocilium displacement suggested that USH1G is essential for forming the hair cell's kinocilial links. Consistent with other Usher type 1 models, Ush1g^bw/bw mice had no substantial retinal degeneration compared with Ush1g^bw/+ controls. In contrast to previously described Ush1g alleles, this new allele provides the first knockout model for this gene.