The Holling Type II Population Model Subjected to Rapid Random Attacks of Predator

We present the analysis of a mathematical model of the dynamics of interacting predator and prey populations with the Holling type random trophic function under the assumption of random time interval passage between predator attacks on prey. We propose a stochastic approximation algorithm for quantitative analysis of the above model based on the probabilistic limit theorem. If the predators’ gains and the time intervals between predator attacks are sufficiently small, our proposed method allows us to derive an approximative average dynamical system for mathematical expectations of population dynamics and the stochastic Ito differential equation for the random deviations from the average motion. Assuming that the averaged dynamical system is the classic Holling type II population model with asymptotically stable limit cycle, we prove that the dynamics of stochastic model may be approximated with a two-dimensional Gaussian Markov process with unboundedly increasing variances.

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Hydrodynamic Models of Low-Mass Pulsating Supergiants with Radiative Transfer

International Astronomical Union Colloquium ◽

10.1017/s0252921100011726 ◽

1989 ◽

Vol 111 ◽

pp. 264-264

Author(s):

A.B. Foken

Keyword(s):

Radiative Transfer ◽

Variable Star ◽

Stable Limit Cycle ◽

Light Curves ◽

Transfer Model ◽

Stable Limit ◽

Type Ii ◽

Hydrodynamic Models ◽

Stellar Pulsations ◽

Low Mass

AbstractA method of calculating nonlinear stellar pulsations including nonstationary radiative transfer in a grey spherical atmosphere is described. With the help of this method eleven type II supergiant radiative models were constructed with masses of 0.6M⊙, luminosities ranging from 128L⊙ to 3123L⊙ and periods in the range from 1.123 to 46 days. A stable limit cycle was found to be accessible only by models with an effective temperature between 5700K and 6165K. The model with Te = 6165K is stable, whereas the models cooler than 5700K show nonregular behavior. Transition from strictly periodic to nonregular pulsation arises when M/R ≲ 0.018, due to high amplitudes, δr/r ≈ 1, and strong shocks in the atmosphere. The radiative transfer effects lead to some decay in the radial amplitude, as well as to a more significant decrease, about 0.6 magnitudes, in the light variation. A photometric comparison between the light curves of the models calculated with and without transfer and the observed light curve of the variable star No. 154 in M3 shows that the results predicted by the transfer model are in much better agreement with obervational data.

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FEEDBACK-INDUCED COMPLEX DYNAMICS IN A TWO-COMPONENT REGULATORY CIRCUIT

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412500599 ◽

2012 ◽

Vol 22 (03) ◽

pp. 1250059 ◽

Cited By ~ 1

Author(s):

HUAHAI QIU ◽

TIANSHOU ZHOU

Keyword(s):

Negative Feedback ◽

First Passage Time ◽

Stable Limit Cycle ◽

Feedback Loops ◽

Type I ◽

Stable Limit ◽

Type Ii ◽

Negative Feedback Loops ◽

Two Component ◽

Positive And Negative Feedback

Coupled positive and negative feedback loops form an essential building block of cellular signaling pathways, but the dynamics of such a system remain to be fully explored. Here, we systematically analyze a two-component circuit with interlinked positive and negative feedback loops, focusing on feedback-induced dynamics and their mechanisms. We show that feedbacks can induce monostability, oscillation, and excitability as well as the coexistence of two attractors (including that of two different stable steady states (called Type-I bistability) and that of both a stable steady state and a stable limit cycle (called Type-II bistability)). In particular for Type-II bistability, we find that feedback-controlled molecular noise can induce stochastic switching between two different attractors, and that the first passage time between them exhibits a multi-peak distribution. These investigations provide insights for understanding the biological functions of coupled positive and negative feedback circuits from the viewpoint of dynamics.

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Estimation of oscillation velocities of oscillator network

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2018-32-17 ◽

2018 ◽

Vol 32 ◽

pp. 182-189

Author(s):

Volodymyr Shcherbak ◽

Iryna Dmytryshyn

Keyword(s):

Dynamical System ◽

Nonlinear Oscillations ◽

Initial Conditions ◽

Nonlinear Dynamical System ◽

Stable Limit Cycle ◽

Nonlinear Observer ◽

Stable Limit ◽

Nonlinear Dynamical ◽

Biomechanical Models ◽

Neural Ensembles

The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

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COEXISTENCE OF POINT, PERIODIC AND STRANGE ATTRACTORS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413500934 ◽

2013 ◽

Vol 23 (05) ◽

pp. 1350093 ◽

Cited By ~ 116

Author(s):

JULIEN CLINTON SPROTT ◽

XIONG WANG ◽

GUANRONG CHEN

Keyword(s):

Dynamical System ◽

Differential Equations ◽

Strange Attractor ◽

Chaotic Attractor ◽

Stable Equilibrium ◽

Stable Limit Cycle ◽

Stable Limit ◽

New Chaotic System ◽

Point Attractor ◽

New System

For a dynamical system described by a set of autonomous ordinary differential equations, an attractor can be a point, a periodic cycle, or even a strange attractor. Recently, a new chaotic system with only one stable equilibrium was described, which locally converges to the stable equilibrium but is globally chaotic. This paper further shows that for certain parameters, besides the point attractor and chaotic attractor, this system also has a coexisting stable limit cycle, demonstrating that this new system is truly complicated and interesting.

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METABOLIC STUDIES WITH 131I-LABELED THYROXINE. II.

Acta Endocrinologica ◽

10.1530/acta.0.0440475 ◽

1963 ◽

Vol 44 (3) ◽

pp. 475-480 ◽

Cited By ~ 1

Author(s):

R. Grinberg

Keyword(s):

Spinal Cord ◽

Central Nervous System ◽

Nervous System ◽

Optic Nerve ◽

Pituitary Gland ◽

Time Interval ◽

Time Intervals ◽

Pituitary Glands ◽

The Central Nervous System ◽

Tentative Explanation

ABSTRACT Radiologically thyroidectomized female Swiss mice were injected intraperitoneally with 131I-labeled thyroxine (T4*), and were studied at time intervals of 30 minutes and 4, 28, 48 and 72 hours after injection, 10 mice for each time interval. The organs of the central nervous system and the pituitary glands were chromatographed, and likewise serum from the same animal. The chromatographic studies revealed a compound with the same mobility as 131I-labeled triiodothyronine in the organs of the CNS and in the pituitary gland, but this compound was not present in the serum. In most of the chromatographic studies, the peaks for I, T4 and T3 coincided with those for the standards. In several instances, however, such an exact coincidence was lacking. A tentative explanation for the presence of T3* in the pituitary gland following the injection of T4* is a deiodinating system in the pituitary gland or else the capacity of the pituitary gland to concentrate T3* formed in other organs. The presence of T3* is apparently a characteristic of most of the CNS (brain, midbrain, medulla and spinal cord); but in the case of the optic nerve, the compound is not present under the conditions of this study.

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Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽

10.2298/fil1716271p ◽

2017 ◽

Vol 31 (16) ◽

pp. 5271-5293

Author(s):

A.K. Pal ◽

P. Dolai ◽

G.P. Samanta

Keyword(s):

Equilibrium Points ◽

Stable Limit Cycle ◽

Limit Cycle Oscillation ◽

Toxic Substances ◽

Stable Limit ◽

Biological Parameters ◽

Delay Model ◽

Competitive System ◽

Interval Numbers ◽

Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

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Neural Network Approach for Global Solar Irradiance Prediction at Extremely Short-Time-Intervals Using Particle Swarm Optimization Algorithm

Energies ◽

10.3390/en14041213 ◽

2021 ◽

Vol 14 (4) ◽

pp. 1213

Author(s):

Ahmed Aljanad ◽

Nadia M. L. Tan ◽

Vassilios G. Agelidis ◽

Hussain Shareef

Keyword(s):

Neural Networks ◽

Particle Swarm Optimization ◽

Solar Irradiance ◽

Particle Swarm ◽

Time Interval ◽

Time Intervals ◽

Swarm Optimization ◽

Backpropagation Neural Networks ◽

Proposed Model ◽

Short Time

Hourly global solar irradiance (GSR) data are required for sizing, planning, and modeling of solar photovoltaic farms. However, operating and controlling such farms exposed to varying environmental conditions, such as fast passing clouds, necessitates GSR data to be available for very short time intervals. Classical backpropagation neural networks do not perform satisfactorily when predicting parameters within short intervals. This paper proposes a hybrid backpropagation neural networks based on particle swarm optimization. The particle swarm algorithm is used as an optimization algorithm within the backpropagation neural networks to optimize the number of hidden layers and neurons used and its learning rate. The proposed model can be used as a reliable model in predicting changes in the solar irradiance during short time interval in tropical regions such as Malaysia and other regions. Actual global solar irradiance data of 5-s and 1-min intervals, recorded by weather stations, are applied to train and test the proposed algorithm. Moreover, to ensure the adaptability and robustness of the proposed technique, two different cases are evaluated using 1-day and 3-days profiles, for two different time intervals of 1-min and 5-s each. A set of statistical error indices have been introduced to evaluate the performance of the proposed algorithm. From the results obtained, the 3-days profile’s performance evaluation of the BPNN-PSO are 1.7078 of RMSE, 0.7537 of MAE, 0.0292 of MSE, and 31.4348 of MAPE (%), at 5-s time interval, where the obtained results of 1-min interval are 0.6566 of RMSE, 0.2754 of MAE, 0.0043 of MSE, and 1.4732 of MAPE (%). The results revealed that proposed model outperformed the standalone backpropagation neural networks method in predicting global solar irradiance values for extremely short-time intervals. In addition to that, the proposed model exhibited high level of predictability compared to other existing models.

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Real-World Experience with Artificial Intelligence-Based Triage in Transferred Large Vessel Occlusion Stroke Patients

Cerebrovascular Diseases ◽

10.1159/000515320 ◽

2021 ◽

pp. 1-6

Author(s):

Jacob R. Morey ◽

Xiangnan Zhang ◽

Kurt A. Yaeger ◽

Emily Fiano ◽

Naoum Fares Marayati ◽

...

Keyword(s):

Artificial Intelligence ◽

Clinical Outcomes ◽

Warning System ◽

Large Vessel ◽

Time Interval ◽

Large Vessel Occlusion ◽

Time Intervals ◽

Vessel Occlusion ◽

Left Behind ◽

Stroke Center

Background and Purpose: Randomized controlled trials have demonstrated the importance of time to endovascular therapy (EVT) in clinical outcomes in large vessel occlusion (LVO) acute ischemic stroke. Delays to treatment are particularly prevalent when patients require a transfer from hospitals without EVT capability onsite. A computer-aided triage system, Viz LVO, has the potential to streamline workflows. This platform includes an image viewer, a communication system, and an artificial intelligence (AI) algorithm that automatically identifies suspected LVO strokes on CTA imaging and rapidly triggers alerts. We hypothesize that the Viz application will decrease time-to-treatment, leading to improved clinical outcomes. Methods: A retrospective analysis of a prospectively maintained database was assessed for patients who presented to a stroke center currently utilizing Viz LVO and underwent EVT following transfer for LVO stroke between July 2018 and March 2020. Time intervals and clinical outcomes were compared for 55 patients divided into pre- and post-Viz cohorts. Results: The median initial door-to-neuroendovascular team (NT) notification time interval was significantly faster (25.0 min [IQR = 12.0] vs. 40.0 min [IQR = 61.0]; p = 0.01) with less variation (p < 0.05) following Viz LVO implementation. The median initial door-to-skin puncture time interval was 25 min shorter in the post-Viz cohort, although this was not statistically significant (p = 0.15). Conclusions: Preliminary results have shown that Viz LVO implementation is associated with earlier, more consistent NT notification times. This application can serve as an early warning system and a failsafe to ensure that no LVO is left behind.

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Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽

10.3390/fluids3030063 ◽

2018 ◽

Vol 3 (3) ◽

pp. 63 ◽

Cited By ~ 3

Author(s):

Thomas Meunier ◽

Claire Ménesguen ◽

Xavier Carton ◽

Sylvie Le Gentil ◽

Richard Schopp

Keyword(s):

Normal Mode ◽

Growth Rates ◽

Time Interval ◽

Time Intervals ◽

Horizontal Structure ◽

Azimuthal Wave ◽

Wave Numbers ◽

Non Linear ◽

Long Time ◽

Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

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FACTORS INVOLVED IN THE PRODUCTION OF IMMUNITY WITH PNEUMOCOCCUS VACCINE

Journal of Experimental Medicine ◽

10.1084/jem.48.1.83 ◽

1928 ◽

Vol 48 (1) ◽

pp. 83-104 ◽

Cited By ~ 7

Author(s):

Alvan L. Barach ◽

Keyword(s):

Intact Cell ◽

Broth Culture ◽

Time Interval ◽

Type I ◽

Type Ii ◽

Lobar Pneumonia ◽

The Common ◽

Immunity Mechanism ◽

Lethal Doses ◽

Pneumococcus Type

1. The antigenic function of a pneumococcus vaccine made from the intact cell was compared with that derived fron a watery extract of the cell free from formed elements. In each instance, the immunity produced was dependent upon type-specific protective substance and not upon the elaboration of the common protein antibody. 2. The vaccine made from the intact cell resulted in both active and passive immunity which began on the 3rd day, increased markedly to the 5th, and remained approximately stationery to the 7th day. In the case of the Berkefeld filtrate of the shaken bacteria and the filtrate of the broth culture, the immunity began on the 4th day, increased to the 5th, and remained approximately stationery to the 7th day. The immunity produced by Pneumococcus Type I vaccine is greater than that produced by Type II. On the 3rd day, mice vaccinated with Type I vaccine resisted 100,000 minimal lethal doses, whereas mice immunized with Type II resisted 10,000 minimal lethal doses. On the 5th day, a larger percentage of mice survived these doses than on the 3rd day. 3. Certain factors related to the preparation and dosage of the vaccine are discussed. 4. As far as the time interval and the degree of immunity produced are concerned, these results suggest the possibility of employing pneumococcus vaccine in suitable doses in the treatment of lobar pneumonia. That an earlier activity of the immunity mechanism could actually be initiated in a patient with lobar pneumonia has still to be demonstrated.

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