scholarly journals Multiple Nonlinear Oscillations in a𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Haijun Hu ◽  
Li Liu ◽  
Jie Mao
Keyword(s):  
Bifurcation Theory ◽  
Nonlinear Oscillations ◽  
Coupled System ◽  
Simultaneous Occurrence ◽  
Multiple Periodic Solutions ◽  
Equivariant Bifurcation Theory ◽  
The Individual ◽  
Delay Differential ◽  
Theoretical Results ◽  
Linear Decay

A coupled system of nine identical cells with delays and𝔻3×𝔻3-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.

scholarly journals Synchronized Tick Population Oscillations Driven by Host Mobility and Spatially Heterogeneous Developmental Delays Combined

2021 ◽  
Vol 83 (6) ◽  
Author(s):  
Xue Zhang ◽  
Jianhong Wu
Keyword(s):  
Delay Differential Equations ◽  
Developmental Delays ◽  
Coupled System ◽  
Single Species ◽  
Adult Tick ◽  
Life Cycles ◽  
Positive Equilibrium ◽  
Tick Population ◽  
Host Mobility ◽  
Delay Differential

AbstractWe consider a coupled system of delay differential equations for a single-species tick population dynamics, assuming feeding adult ticks are distributed by their hosts in a spatially heterogeneous environment consisting of two patches where egg ticks produced will complete their life cycles with different, normal and diapause, developmental delays. We show that the mobility of adult tick host and the diapause developmental delay combined drive a synchronized oscillation in the total tick populations around a uniquely defined positive equilibrium, and this synchronization makes the oscillatory patterns much simpler in comparison with multi-peak oscillations exhibited in the absence of host mobility.

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

Bogdanov–Takens and Triple Zero Bifurcations of Coupled van der Pol–Duffing Oscillators with Multiple Delays

2017 ◽  
Vol 27 (09) ◽  
pp. 1750133 ◽  
Author(s):  
Xia Liu ◽  
Tonghua Zhang
Keyword(s):  
Delay Differential Equations ◽  
Time Delays ◽  
Normal Forms ◽  
Multiple Delays ◽  
Third Order ◽  
Van Der Pol ◽  
Normal Form Theory ◽  
Form Theory ◽  
Delay Differential ◽  
Theoretical Results

In this paper, the Bogdanov–Takens (B–T) and triple zero bifurcations are investigated for coupled van der Pol–Duffing oscillators with [Formula: see text] symmetry, in the presence of time delays due to the intrinsic response and coupling. Different from previous works, third order unfolding normal forms associated with B–T and triple zero bifurcations are needed, which are obtained by using the normal form theory of delay differential equations. Numerical simulations are also presented to illustrate the theoretical results.

scholarly journals Wicksell's Problem in Local Stereology

2013 ◽  
Vol 45 (4) ◽  
pp. 925-944
Author(s):  
Ó. Thórisdóttir ◽  
M. Kiderlen
Keyword(s):  
Reference Point ◽  
Simulated Data ◽  
Domain Of Attraction ◽  
Spherical Particles ◽  
Section Profile ◽  
Particle Parameters ◽  
The Individual ◽  
The Relationship ◽  
Theoretical Results ◽  
Isotropic Random

Wicksell's classical corpuscle problem deals with the retrieval of the size distribution of spherical particles from planar sections. We discuss the problem in a local stereology framework. Each particle is assumed to contain a reference point and the individual particle is sampled with an isotropic random plane through this reference point. Both the size of the section profile and the position of the reference point inside the profile are recorded and used to recover the distribution of the corresponding particle parameters. Theoretical results concerning the relationship between the profile and particle parameters are discussed. We also discuss the unfolding of the arising integral equations, uniqueness issues, and the domain of attraction relations. We illustrate the approach by providing reconstructions from simulated data using numerical unfolding algorithms.

scholarly journals A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

2014 ◽  
Vol 9 ◽  
pp. 53-68 ◽  
Author(s):  
B. El Boukari ◽  
N. Yousfi
Keyword(s):  
Reproduction Number ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Intracellular Delay ◽  
Immunodeficiency Virus ◽  
Delay Differential ◽  
Theoretical Results ◽  
Disease Free

In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely defined by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay affects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.

scholarly journals Multicell Power Supplies for Improved Energy Efficiency in the Information and Communications Technology Infrastructures

2021 ◽  
Author(s):  
Michael Chrysostomou ◽  
Nicholas Christofides ◽  
Stelios Ioannou ◽  
Alexis Polycarpou
Keyword(s):  
Energy Demand ◽  
Information And Communications Technology ◽  
Power Supplies ◽  
Communications Technology ◽  
Cell Structures ◽  
Full Power ◽  
Overall Efficiency ◽  
Simulation Results ◽  
The Individual ◽  
Theoretical Results

The rapid growth of the Information and Communications Technology (ICT) sector requires additional infrastructure, such as more micro-datacenters and telecom stations, to support the higher internet speeds and low latency requirements of 5G net-works. The increased power requirements of the new ICT technologies necessitate the proposal of new power supplies in an attempt to retain the increase in energy demand and running costs. This work provides an in-depth theoretical analysis on the losses of the individual stages of commercially available PSU and proposes a new multicell PSU, Buck-PFC converter, which offers a higher overall efficiency at varying load levels. The theoretical results are verified using simulation results, via PSIM Thermal Module, and using experimental data. The results indicate that multi-cell structures can improve the overall PSU ef-ficiency by 1.2% at 50% rated power and more than 2.1% at full power. Finally, taking into consideration the economic implica-tions of this study, it is shown that the proposed multicell structure may increase the PSU costs by 10.78% but the payback pe-riod is in the order of just 3.3 years.

scholarly journals Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yuanyuan Chen ◽  
Ya-Qing Bi
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Theory ◽  
Center Manifold ◽  
Local Analysis ◽  
Normal Form Theory ◽  
Form Theory ◽  
Vector Borne ◽  
The Stability ◽  
Delay Differential

A delay-differential modelling of vector-borne is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument.

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