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1.
Melnikov analysis of chaos in a simple epidemiological model   总被引:4,自引:0,他引:4  
 Melnikov’s method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model. Received 8 August 1995; received in revised form 21 November 1995  相似文献   

2.
The goal of this study is to (a) find the most predictive anthropometric factors, (b) check the predictability of a new jumping motor test, and (c) predict Fosbury-flop (FFP) performance by using a multiregression analysis. The participants of this study were 49 girls (age 13.6 ± 0.48 years; height = 1.61 ± 0.07 m) and 68 boys (age 13.6 ± 0.47 years; height = 1.64 ± 0.10 m). We measured the height, the sitting height), the highest position touched by the hand in a standing position (HEIGHTARM), the highest position touched by the hand during a running 1-leg vertical jump with a semirestricted curved run-up (HMAX), and the best performance in the FFP. We then calculated the leg length (LEGLENGTH), the skelic index (ratio of legs length to the abdomen length, SKEL), the vertical performance (VP, difference between HMAX and HEIGHTARM). The ability level was deducted from the difference between (LEGLENGTH + VP) and FFP. Pearson correlation coefficients were calculated, and a multiple-regression analysis technique was applied to find the most predictive model (p < 0.05). The FFP was correlated with standing height (HEIGHT; r = 0.398; p < 0.05), HMAX (r = 0.707; p < 0.0005), ABILITY (r = 0.391; p < 0.005) but not with SKEL (r = 0.161; p = 0.01). The best multiple-regression model included HEIGHT, HMAX, and ABILITY with a high level of prediction (r2 = 0.94). In conclusion, the FFP performance can be predicted with equation: FFP = -0.618 HEIGHT + 0.898 HMAX + 0.669 ABILITY - 0.08. This equation is quite similar for both sexes, showing that 13-year-old girls and boys use the same method to jump high, which implies that the way to increase coordination or lower limb strength during training can be the same for junior boys and girls in high jump.  相似文献   

3.
A first-order difference equation which constitutes a simple model for a lethal parasite-host interaction is studied. Completing a study initiated by May and Anderson, the dynamics are shown to be completely chaotic.  相似文献   

4.
The effects of pharmacological interventions that modulate Ca2+ homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca2+] in the cytosol, [Ca2+] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca2+ stores and transmembrane ion fluxes via K+ channels, Cl channels, and voltage-operated Ca2+ channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca2+] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.  相似文献   

5.
 We modify a simple mathematical model for natural selection originally formulated by Robert M. May in 1983 by permitting one homozygote to have a larger selective advantage when rare than the other, and show that the new model exhibits dynamical chaos. We determine an open region of parameter space associated with homoclinic points, and prove that there are infinite sequences of period-doubling bifurcations along selected paths through parameter space. We also discuss the possibility of chaos arising from imbalance in the homozygote fitnesses in more realistic biological situations, beyond the constraints of the model. Received 3 February 1995; received in revised form 1 November 1995  相似文献   

6.
For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303-306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.  相似文献   

7.
Chaotic regimens have been observed experimentally in neurons as well as in deterministic neuronal models. The R15 bursting cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. Previously, the model of Plant and Kim has been shown to exhibit both bursting and beating modes of electrical activity. In this report, we demonstrate (a) that a chaotic regime exists between the bursting and beating modes of the model, and (b) that the model approaches chaos from both modes by a period doubling cascade. The bifurcation parameter employed is the external stimulus current. In addition to the period doubling observed in the model-generated trajectories, a period three "window" was observed, power spectra that demonstrate the approaches to chaos were generated, and the Lyaponov exponents and the fractal dimension of the chaotic attractors were calculated. Chaotic regimes have been observed in several similar models, which suggests that they are a general characteristic of cells that exhibit both bursting and beating modes.  相似文献   

8.
Gánti's chemoton model (Gánti, T., 2002. On the early evolution of biological periodicity. Cell. Biol. Int. 26, 729) is considered as an iconic example of a minimal protocell including three key subsystems: membrane, metabolism and information. The three subsystems are connected through stoichiometrical coupling which ensures the existence of a replication cycle for the chemoton. Our detailed exploration of a version of this model indicates that it displays a wide range of complex dynamics, from regularity to chaos. Here, we report the presence of a very rich set of dynamical patterns potentially displayed by a protocell as described by this implementation of a chemoton-like model. The implications for early cellular evolution and synthesis of artificial cells are discussed.  相似文献   

9.
Using the mathematical model of the pacemaker neuron formulated by Chay, we have investigated the conditions in which a neuron can generate chaotic signals in response to variation in temperature, ionic compositions, chemicals, and the strength of applied depolarizing current.This work was supported by NSF PCM82 15583  相似文献   

10.
Summary A modified version of the Oregonator is analysed as a model of oscillations, bistability and chaos in the bromate-malonic acid-cerium reaction.This study was supported by the National Cancer Institute, USA, Grant No. 5 F32 CAO5152-02.  相似文献   

11.
12.
The behavior of a model that generalizes the Lotka-Volterra problem into three dimensions is presented. The results show the analytic derivation of stability diagrams that describe the system's qualitative features. In particular, we show that for a certain value of the bifurcation parameter the system instantly jumps out of a steady state solution into a chaotic solution that portrays a fractal torus in the three-dimensional phase space. This scenario, is referred to as the explosive route to chaos and is attributed to the non-transversal saddle connection type bifurcation. The stability diagrams also present a region in which the Hopf type bifurcation leads to periodic and chaotic solutions. In addition, the bifurcation diagrams reveal a qualitative similarity to the data obtained in the Texas and Bordeaux experiments on the Belousov-Zhabotinskii chemical reaction. The paper is concluded by showing that the model can be useful for representing dynamics associated with biological and chemical phenomena.  相似文献   

13.
A topological approach is presented for the analysis of control and regulation in metabolic pathways. In this approach, the control structure of a metabolic pathway is represented by a weighted directed graph. From an inspection of the topology of the graph, the control coefficients of the enzymes are evaluated in a heuristic manner in terms of the enzyme elasticities. The major advantage of the topological approach is that it provides a visual framework for (1) calculating the control coefficients of the enzymes, (2) analyzing the cause-effect relationships of the individual enzymes, (3) assessing the relative importance of the enzymes in metabolic regulation, and (4) simplifying the structure of a given pathway, from a regulatory viewpoint. Results are obtained for (a) an unbranched pathway in the absence of feedback the feedforward regulation and (b) an unbranched pathway with feedback inhibition. Our formulation is based on the metabolic control theory of Kacser and Burns (1973) and Heinrich and Rapoport (1974).  相似文献   

14.
Topological analysis of enzymic mechanisms   总被引:1,自引:0,他引:1  
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15.
A graphical analysis demonstrates the ability of slow substrate activation and certain types of cooperativity between the two enzyme active sites to generate sustained oscillations. The analysis allows us to estimate kinetic parameter values for which oscillations exist. The scheme analyzed can explain the cyclical changes in functioning of various motor enzymes. Moreover, this scheme does not generate bistability for any parameter values. The graphical analysis presented is simple and visually clarifies the regulatory role of the details in the kinetic schemes.  相似文献   

16.
17.
A three-variable model of a continuous fermentation process characterised by product inhibition is studied. It is shown that if the cell to substrate yield is constant, the system cannot have periodic solutions. If, on the other hand, the yield term is a variable function of substrate concentration, the model will exhibit oscillations in the cells, substrate and product concentrations in the form of Hopf bifurcation in the underlying system of three nonlinear, ordinary differential equations which comprise the model.  相似文献   

18.
19.
Forty-seven birds (M/F = 33/14) with natural outbreak dilated cardiomyopathy (DCM) of right ventricle (RV) and 33 birds with artificially cool-induced DCM hearts were studied. Clinically, 20 severe and 13 mild DCM cases were induced during five weeks and the peak morbidity was in the 2nd week. The progressive dilatation of RV and hypokinesis of septum was shown by echocardiography. At autopsy, the ratio of heart weights to the body weights was increased, the ratio of RV weight to the total ventricle significantly increased, especially in the severe DCM cases (P < 0.05). The RV was dilated and the wall thickness was increased and finally both RV and left ventricle (LV) were markedly dilated and the septum became thinner. The struts, weave and coil demonstrated by silver impregnation stain were fragmented, dissociated and overstretched. The promatrix metalloproteinases (MMP)-2, -9 and active MMP-2 were markedly increased in natural outbreak DCM cases, especially in the RV (P < 0.05). The proMMP-2 and active MMP-2 was increased in the cool induced DCM cases, especially in the RV of severe DCM (P < 0.05). These indicated that both the natural outbreak and the artificially induced DCM of broiler chickens are ideal DCM animal models.  相似文献   

20.
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