Application of interval iterations to the entrainment problem in respiratory physiology

2009 ◽  
Vol 367 (1908) ◽  
pp. 4717-4739 ◽  
Author(s):  
Jacques Demongeot ◽  
Jules Waku
Keyword(s):  
Population Dynamics ◽  
Limit Cycles ◽  
Numerical Results ◽  
Respiratory Physiology ◽  
New Type ◽  
Classical Point ◽  
Interval Iterations ◽  
Asymptotic Behaviours

We present here some theoretical and numerical results about interval iterations. We consider first an application of the interval iterations theory to the problem of entrainment in respiratory physiology for which the classical point iterations theory fails. Then, after a brief review of some of the main aspects of point iterations, we explain what is meant by the term ‘interval iterations’. It consists essentially in replacing in the point iterations the function to iterate by a set-valued map. We present both theoretical and numerical aspects of this new type of iterations and we observe the dynamical behaviours encountered, such as fixed intervals and interval limit cycles. The comparison between point and interval iterations is carried out with respect to a parameter ε , which determines the thickness of a neighbourhood around the function to iterate. We will finally focus our attention on the Verhulst and Ricker functions largely used in population dynamics, which exhibit various asymptotic behaviours.

scholarly journals Testing predator - prey theory by studying fluctuating populations of small mammals.

1995 ◽  
Vol 22 (1) ◽  
pp. 89 ◽  
Author(s):  
S. Boutin
Keyword(s):  
Population Dynamics ◽  
Small Mammals ◽  
Limit Cycles ◽  
Functional Responses ◽  
Predator Satiation ◽  
Linear Type ◽  
Small Component ◽  
Wide Range ◽  
Fluctuating Populations

Fluctuating populations of small mammals provide an excellent opportunity to study the functional and numerical responses of predators because of the wide range in prey density that occurs. I reinterpret data from six studies that have examined the role of predation in the population dynamics of voles in California, southern Sweden and western Finland, of snowshoe hares in northern Canada, and of house mice and rabbits in Australia. Most studies have measured functional responses by relying on changes in diet as reflected by scat or stomach contents. These methods are probably biased toward showing predator satiation. Contrary to previous conclusions I find that there is little evidence for non-linear (Type 111) functional-response curves or predator satiation at high prey densities. Recent studies indicate that the functional and numerical responses of predators can be rapid and strong enough to initiate cyclic declines, dampen fluctuations, or even cause stable numbers. The exception to this appears to be the irruptions of mice and rabbits in Australia. I propose a general explanation for the role of predation whereby the effect of predation is largely dependent on the entire prey community. When potentially cyclic prey are a small component of the overall prey biomass, generalist predators are able to prevent fluctuations by strong functional or numerical responses. As the prey community becomes dominated by a few species that fluctuate, limit cycles predominate. Limit cycles turn into irruptive population dynamics when seasonal prey reproduction is eliminated because of extended periods of vegetation growth (vegetation flushes following drought). In the future we must test assumptions underlying the way we study predation by telemetric monitoring of prey mortality and by experimentally manipulating predation.

scholarly journals Approximation properties of the new type generalized Bernstein-Kantorovich operators

2021 ◽  
Vol 7 (3) ◽  
pp. 3826-3844
Author(s):  
Mustafa Kara ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Type Theorem ◽  
Numerical Results ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
New Type ◽  
Kantorovich Operators

<abstract><p>In this paper, we introduce new type of generalized Kantorovich variant of $ \alpha $-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $ \alpha $-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.</p></abstract>

Multi-Dimensional Heterogeneous Resonance Integral Tables Generated for Embedded Self-Shielding Method Towards Irregular Lattices

2018 ◽  
Author(s):  
Qian Zhang ◽  
Qiang Zhao ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Zheng Zheng
Keyword(s):  
Extra Dimension ◽  
Density Ratio ◽  
Numerical Results ◽  
Resonance Integral ◽  
Number Density ◽  
New Type ◽  
Optical Radius

The concept of multi-dimensional heterogeneous resonance integral tables is proposed. The new type of resonance integral is designed for different fuel pins appearing in one lattice with two extra dimension of optical radius and number density ratio in the fuel. Numerical results show that this treatment improves the accuracy of embedded self-shielding method on irregular lattices.

scholarly journals On the anticrowding population dynamics taking into account a discrete set of offspring

2015 ◽  
Vol 56 ◽  
Author(s):  
Šarūnas Repšys ◽  
Vladas Skakauskas
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Type A ◽  
Numerical Results ◽  
Integral Type ◽  
Partial Differential ◽  
Directed Diffusion

A model of a population dynamics is solved numerically taking into account a discrete set of offsprings and the nonlinear (directed) diffusion. The model consists of a system of integro-partial differential equations subject to conditions of integral type. A spread of initially lokalized population is studied. Some numerical results are discussed.

Analysis of New Type Repulsion Mechanism Performance

2012 ◽  
Vol 192 ◽  
pp. 154-158
Author(s):  
Yong Sheng Xu ◽  
Li Kong
Keyword(s):  
Numerical Simulations ◽  
Experimental Verification ◽  
Numerical Results ◽  
Circuit Parameter ◽  
Multiple Series ◽  
Simple Method ◽  
New Type

Using circuit method to analysis equations of circuit and motion of coil-coil Mechanism, numerical simulations were also made. Simple method of experimental verification was proposed. The numerical results show influence of circuit parameter and benefits of multiple series gaps.

One New Kind of Worming Pipe Robot

2014 ◽  
Vol 536-537 ◽  
pp. 944-948
Author(s):  
Feng Ping Xu ◽  
Yan Zhou ◽  
Zhi Cong Zhao
Keyword(s):  
Design Theory ◽  
Simulation Analysis ◽  
Well Logging ◽  
Virtual Prototype ◽  
Numerical Results ◽  
Kinematical Model ◽  
New Type ◽  
Set Up ◽  
Driving Torque ◽  
Kinematical Simulation

Aim at special requirements and limitations of new type carrying technique for special technology well logging, one new type worming pipe robot was put forward based on combination mechanism, it can be used in the new type carrying technique. The walking principle of the robot was given and walking kinematical model and driving torque model were set up in this paper. Further more the virtual prototype was made and kinematical simulation analysis had been accomplished. The numerical results validated the design theory and analysis conclusions of the robot were correct. The robot can have bigger tensile draw.

On a new type of bifurcation of limit cycles for a planar cubic system

1999 ◽  
Vol 36 (2) ◽  
pp. 139-149 ◽  
Author(s):  
J. Chavarriga ◽  
H. Giacomini ◽  
J. Giné
Keyword(s):  
Limit Cycles ◽  
Bifurcation Of Limit Cycles ◽  
Cubic System ◽  
New Type

A Study on the Influence of Hole’s Diameter With Holed Casing Treatment

2011 ◽  
Author(s):  
Wei Xu ◽  
Tong Wang ◽  
Chuangang Gu ◽  
Liang Ding
Keyword(s):  
Centrifugal Compressor ◽  
Numerical Results ◽  
Radial Position ◽  
Bypass Flow ◽  
Stall Margin ◽  
Casing Treatment ◽  
Velocity Magnitude ◽  
Adaptive Effect ◽  
New Type ◽  
Self Adaptive

The holed casing treatment is a new type of casing treatment with self-adaptability for centrifugal compressor with unshrouded impellers. It is demonstrated experimentally and numerically that both of the stall margin and the choked margin of the compressor can be expanded by the treatment. Numerical results indicate that there is a reinjected flow in the holes when the compressor works at low flowrate conditions and a bypass flow at high flowrate conditions. Hole’s diameter is an important parameter for the holed casing treatment. Five cases of different diameter (1.0mm, 1.5mm, 2.0mm, 2.5mm and 3.0mm) were carried out to reveal its influence. Both the stall margin and efficiency are improving with increasing of the hole’s diameter in the cases of diameter below than 2.5mm. At diameter of 2.5mm, the stall margin increment and the efficiency of the compressor are the highest among all 5 cases. However, in the case of 3.0mm, the stable working range enhancing as well as the efficiency is weakened because the velocity magnitude of the reinjected flow decreases. Therefore a key principle of choosing the diameter and the radial position of the hole is presented in the paper to get the best self-adaptive effect: enhancing stable running range as much as possible and keeping higher efficiency.

scholarly journals Scale-invariant localization using quasi-semantic object landmarks

2021 ◽  
Author(s):  
Andrew Holliday ◽  
Gregory Dudek
Keyword(s):  
State Of The Art ◽  
Visual Localization ◽  
Visual Feature ◽  
Scale Invariant ◽  
Object A ◽  
Change Factors ◽  
Major Scale ◽  
New Type ◽  
Semantic Object ◽  
Classical Point

AbstractThis work presents Object Landmarks, a new type of visual feature designed for visual localization over major changes in distance and scale. An Object Landmark consists of a bounding box $${\mathbf {b}}$$ b defining an object, a descriptor $${\mathbf {q}}$$ q of that object produced by a Convolutional Neural Network, and a set of classical point features within $${\mathbf {b}}$$ b . We evaluate Object Landmarks on visual odometry and place-recognition tasks, and compare them against several modern approaches. We find that Object Landmarks enable superior localization over major scale changes, reducing error by as much as 18% and increasing robustness to failure by as much as 80% versus the state-of-the-art. They allow localization under scale change factors up to 6, where state-of-the-art approaches break down at factors of 3 or more.

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