Dynamical analysis of periodic bursting in piece-wise linear planar neuron model

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.     

Periodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

We obtain necessary and sufficient conditions on the existence of a unique positive equilibrium point and a set of sufficient conditions on the existence of periodic solutions for a 3-dimensional system which arises from a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Our results improve the corresponding results obtained by Hsu, Luo, and Waltman [1]. Received: 20 November 1997 / Revised version: 12 February 1999 / Published online: 20 December 2000     

环境污染下脉冲输入恒化器模型动力学性质的研究

研究了环境污染下脉冲输入恒化器模型的动力学性质,得到了微生物灭绝周期解的全局稳定性和系统的持续生存.     

Resonance of the epidemic threshold in a periodic environment

Resonance between some natural period of an endemic disease and a seasonal periodic contact rate has been the subject of intensive study. This paper does not focus on resonance for endemic diseases but on resonance for emerging diseases. Periodicity can have an important impact on the initial growth rate and therefore on the epidemic threshold. Resonance occurs when the Euler-Lotka equation has a complex root with an imaginary part (i.e., a natural frequency) close to the angular frequency of the contact rate and a real part not too far from the Malthusian parameter. This is a kind of continuous-time analogue of work by Tuljapurkar on discrete-time population models, which in turn was motivated by the work by Coale on continuous-time demographic models with a periodic birth. We illustrate this resonance phenomenon on several simple epidemic models with contacts varying periodically on a weekly basis, and explain some surprising differences, e.g., between a periodic SEIR model with an exponentially distributed latency and the same model but with a fixed latency.     

Anti-control of periodic firing in HR model in the aspects of position,amplitude and frequency

This paper proposes a novel controller to control position, amplitude and frequency of periodic firing activity in Hindmarsh–Rose model based on Hopf bifurcation theory which is composed of linear control gain and nonlinear control gain. First, we select the activation of the fast ion channel as control parameter. Based on explicit criterion of Hopf bifurcation, a series of conditions are obtained to derive the linear gains of controller responsible for control of the location where the periodic firing activity occurs. Then, based on the control parameter, a series of conditions are obtained to derive the nonlinear gains of controller responsible for controlling the amplitude and frequency of periodic firing activity by using center manifold and normal form. Finally, the numerical experiments show that our controller can make the periodic firing activity occur at designed value and control the amplitude and frequency of periodic firing activity by adjusting nonlinear control gain of controller.     

The identification of the periodic behaviour in an epidemic model

In this paper we study a method for the identification of the unknown parameter of the periodic function and also the first component of the state vector, in a mathematical model which describes the evolution of some diseases with an oro-fecal transmission.To solve the identification problem we use a numerical method to integrate the differential equations system, which reproduces the stability properties of the above mentioned continuous system.The numerical methods which we propose can be applied also to a spatial semi discretization of the reaction-diffusion model which is a diffusive generalization of the system that we consider in this paper.Finally, through an analysis on both the continuous and the discrete system we also obtain a necessary condition on the experimental data in order that a periodic trajectory of the system exists.Work supported by: Progetto Finalizzato Controllo Malattie da Infezione-CNR and by Ministero Pubblica Istruzione     

一类具有时滞的生化反应模型的Hopf分支

在生物化工用肺炎杆菌与甘油转化为1,3-丙二醇的过程中会出现振荡现象,本文对出现振荡的机理进行了研究,根据生物意义,在模型中引入了时滞项,经分析和计算得到了产生Hopf分支的分支值以及分支值随控制参数变化的规律,并利用时滞微分方程的数值解法绘制了周期解的图形和相图。为这一过程的振荡机理研究提供了理论依据。并可用于指导工艺控制。     

Numerical study of the stability of some autowave solutions in a mathematical model of blood clotting

The stability of some types of solution for a set of equations representing a blood clotting model is examined using numerical methods of solving perturbation problems and the apparatus of adjoint equations. It is concluded that spiral waves are stable in this system, whereas traveling pulses are unstable at parameters corresponding to a chaotic regime in the punctual problem.     

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer’s disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.     

Toxic HAB species from the Sea of Okhotsk detected by a metagenetic approach,seasonality and environmental drivers

During recent decades, the distribution of harmful algal bloom (HAB) species has expanded worldwide together with the increase of blooms and toxicity events. In this study, the presence of toxic HAB species in the Sea of Okhotsk was investigated based on metagenetic data collected during 6 years of weekly monitoring. Operational taxonomic units (OTUs) associated with the toxic HAB species were detected based on amplifying 18S V7-V9 and 28S D1 rRNA gene regions. In total, 43 unique OTUs associated with toxic HAB species were revealed, with 26 of those previously not reported from the Sea of Okhotsk. More OTUs belonging to dinoflagellates were detected by 18S, whereas a similar number of OTUs associated with dinoflagellates and diatoms were detected by targeting the 28S region. Species belonging to genera Alexandrium, Karenia and Karlodinium were mainly associated with OTUs under Dinophyceae, whereas Bacillariophyceae was represented by the species belonging to genus Pseudo-nitzschia. From the detected OTUs, 22 showed a clear seasonal pattern with the majority of those appearing during summer-autumn. For Alexandrium pacificum, Aureococcus anophagefferens, and Pseudo-nitzschia pungens, the seasonal pattern was detected based on both rRNA regions. Additionally, 14 OTUs were detected during all seasons and two OTUs appeared sporadically. OTUs associated with the toxic species had low relative read abundances, which together with other factors such as similar and variable morphology as well as usage of fixatives, may explain why those species have previously not been detected by light microscopy. Environmental parameters, especially water temperature, significantly (<0.05) influenced the variability in OTU relative abundances and displayed significant (<0.05) correlations with the unique OTUs. The results of this study demonstrate the usefulness of the metagenetic approach for phytoplankton monitoring, which is especially relevant for detecting toxic HAB species.     

陆面模式中根系参数的改进及其对模拟结果的影响

为改进陆面模式中根系的参数化,本文在陆面模式SSiB2玉米农田参数本地化的基础上,将CERES-Maize的根系子模型嵌套到SSiB2模式中,研究2种改进的根系参数化方案对陆气通量模拟结果的影响.结果表明： 当根系模型只为SSiB2模式提供根系深度参数（方案1）时,陆气通量的模拟精度有所提高：整个生育期内,感热通量、潜热通量等的模拟值与观测值的相关系数增大,线性拟合的均方根误差减小;播种后121天 成熟,CO₂通量的模拟精度也有所提高.当根系模型为SSiB2模式同时提供根系深度和根长密度两种参数（方案2）时,上述通量的模拟精度较原SSiB2模式同样得以提高.与方案1相比,方案2考虑因素更为复杂、全面,但陆气通量的模拟效果却反而有所下降.改进的根系参数化方案较原SSiB2模式的根系参数化方案更接近实际,这使陆气通量的模拟精度提高;方案2过分夸大了表层土壤的相对根量,使其模拟效果逊色于方案1.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

SWAT模型参数对土地利用变化的响应及其对不同时间尺度径流模拟的影响

SWAT模型广泛应用于土地利用变化的水文效应评估研究,但土地利用变化是否对模型参数产生影响,进而影响径流模拟效果还有待于进一步分析。以东南沿海福建省山美水库流域为研究区,基于SWAT模型,分别模拟1995年、2005年、2015年土地利用条件下的年、月、日尺度径流过程,采用SWAT-CUP进行参数敏感性分析与自动率定,分别获取1995年、2005年、2015年3种土地利用条件下径流过程模拟的最优参数集,比较参数差异;将3组参数集分别应用到不同土地利用条件,分析参数变化对不同时间尺度径流模拟的影响。结果表明：（1）1995-2015年间,研究区土地利用格局发生了较大变化,主要表现为林地转向园地和建设用地;3期土地利用条件下率定的SWAT模型都能较好地模拟山美水库流域年、月、日尺度径流,其效率系数NS和决定系数R²分别大于0.62和0.78。（2）不同土地利用条件下敏感参数基本一致,敏感参数分别为CN2、SOL_AWC、SOL_K、CANMX、ESCO、GW_DELAY、OV_N,但敏感参数取值随着土地利用变化而变化,其变化规律符合敏感参数的物理意义,变化率基本与土地利用变化强度正相关。（3）由土地利用变化引起的参数变化,对年、月径流模拟的影响较小,对日径流影响显著,且随着土地利用变化强度的增加而增加。     

Simulation analysis to test the influence of model adequacy and data structure on the estimation of genetic parameters for traits with direct and maternal effects

Simulations were used to study the influence of model adequacy and data structure on the estimation of genetic parameters for traits governed by direct and maternal effects. To test model adequacy, several data sets were simulated according to different underlying genetic assumptions and analysed by comparing the correct and incorrect models. Results showed that omission of one of the random effects leads to an incorrect decomposition of the other components. If maternal genetic effects exist but are neglected, direct heritability is overestimated, and sometimes more than double. The bias depends on the value of the genetic correlation between direct and maternal effects. To study the influence of data structure on the estimation of genetic parameters, several populations were simulated, with different degrees of known paternity and different levels of genetic connectedness between flocks. Results showed that the lack of connectedness affects estimates when flocks have different genetic means because no distinction can be made between genetic and environmental differences between flocks. In this case, direct and maternal heritabilities are under-estimated, whereas maternal environmental effects are overestimated. The insufficiency of pedigree leads to biased estimates of genetic parameters.     

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.     

The stabilizing role of the Sabbath in pre-monarchic Israel:a mathematical model

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the “Basic Sabbath Number ש₀”—a critical observance of the Sabbath, or large enough ש₀, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.

Electronic supplementary material

The online version of this article (doi:10.1007/s10867-014-9373-9) contains supplementary material, which is available to authorized users.     

Towards the development of a minimal cell model by generalization of a model of Escherichia coli: use of dimensionless rate parameters.

A model of a minimal cell would be a valuable tool in identifying the organizing principles that relate the static sequence information of the genome to the dynamic functioning of the living cell. Our approach for developing a minimal cell model is to first generalize an existing model of Escherichia coli by expressing reaction rates as ratios to a set of reference parameters. This generalized model is a prototype minimal cell model that will be developed by adding detail to explicitly include each chemical species. We tested the concept of a generalized model by testing the effect of scaling all enzyme-catalyzed reactions in the E. coli model. The scaling has little effect on cellular function for a wide range of kinetic ratios, where the kinetic ratio is defined as the rate of all enzyme-catalyzed reactions in a given model relative to those in the E. coli model.     

The limitations of assessing impacts of land use changes on runoff with a distributed hydrological model: case study of the Hron River

A distributed hydrological model was applied for estimating changes in a runoff regime due to land use changes. The upper Hron river basin, which has an area of 1766 km² and is located in central Slovakia, was selected as the pilot basin. A physically-based rainfall-runoff model with distributed parameters was used for modelling runoff from rainfall and melting snow. The parameters of the model were estimated using climate data from 1981–2000 and from three digital map layers: a land-use map, soil map and digital elevation model. Several scenarios of changes in land use were prepared, and the runoff under the new land use conditions was simulated. Long-term mean annual runoff components and the design maximal mean daily discharges with a return period from 5 to 100 years under the previous and changed land uses were estimated and compared. The simulated runoff changes were confronted with expert judgments and estimates from the literature. Limitations of the use of distributed models for estimating land use changes are discussed.     

Temperature response of parameters of a biochemically based model of photosynthesis. I. Seasonal changes in mature maritime pine (Pinus pinaster Ait.)

Responses of plant processes to temperature may vary according to the time scale on which they are measured. In this study, both short‐term and seasonal responses of photosynthesis to temperature were examined. A field study of seasonal changes in the temperature response of photosynthesis was conducted on two provenances, French and Moroccan, of mature maritime pine (Pinus pinaster Ait.). Measurements were made every 2 months over a 1‐year period and used to parameterize a mechanistic model of photosynthesis. Temperature responses of maximum Rubisco activity, V_cmax, and potential electron transport rate, J_max, were obtained for each measurement period, as was the response of stomatal conductance, g_s, to water vapour pressure deficit (VPD). Absolute values of V_cmax and J_max at 25 °C were related to needle nitrogen content, N_area.N_area, and thus V_cmax and J_max, were negatively correlated with the mean minimum temperature in the month preceding measurements. The ratio of J_max : V_cmax at 25 °C varied between 1 and 1·7 but did not show any seasonal trend. Nor was there any seasonal trend in the relative temperature response of V_cmax, which had an activation energy H_a of approximately 57 kJ mol^?1 throughout the experiment. The activation energy of J_max was also close to constant throughout the experiment, averaging 39 kJ mol^?1. For the French provenance, the optimal temperature of J_max was positively correlated with the maximum temperature of the previous day, but no such correlation was found for the Moroccan provenance. The response of g_s to VPD also varied seasonally, with much stronger stomatal closure in winter months. Taken together, these results implied a translational shift downwards of the photosynthetic temperature response curve with increasing T_prev, and a shift in the temperature optimum of photosynthesis of 5–10 °C between summer and winter. These results illustrate that the short‐term temperature response of photosynthesis varies significantly on a seasonal basis.