Coupling Effects on Synchronizability of Two-Layer Network's Projective Outer Synchronization

2017 ◽  
Vol 873 ◽  
pp. 353-357
Author(s):  
Bo Yu Feng ◽  
Zhi Hao Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Complex Network ◽  
Simulation Experiment ◽  
Small World ◽  
Experimental Results ◽  
Coupling Effects ◽  
Network Synchronization ◽  
Numerical Examples ◽  
Outer Synchronization

Based on nonlinear dynamics theory and knowledge of complex network, this paper expanded the range of two-layer network synchronization to projective outers synchronization. A mathematical model was constructed and feasibility of synchronization was demonstrated. Then we improved the model in order to study the function of different couplings [1]. Numerical examples are examined to compare the synchronizability of projective outer synchronization with different couplings. A rule called "outer small-world effect" was found due to simulation experiment. Finally, some instances were used to explain experimental results.

scholarly journals Outer Synchronization of Simple Firefly Discrete Models in Coupled Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
A. Arellano-Delgado ◽  
C. Cruz-Hernández ◽  
R. M. López Gutiérrez ◽  
C. Posadas-Castillo
Keyword(s):  
Small World ◽  
Discrete Models ◽  
Small World Networks ◽  
Network Synchronization ◽  
Collective Behaviors ◽  
Outer Synchronization ◽  
Complex Systems Theory ◽  
Experimental Implementation ◽  
Coupled Networks ◽  
Discrete Time Dynamical Systems

Synchronization is one of the most important emerging collective behaviors in nature, which results from the interaction in groups of organisms. In this paper, network synchronization of discrete-time dynamical systems is studied. In particular, network synchronization with fireflies oscillators like nodes is achieved by using complex systems theory. Different cases of interest on network synchronization are studied, including for a large number of fireflies oscillators; we consider synchronization in small-world networks and outer synchronization among different coupled networks topologies; for all presented cases, we provide appropriate ranges of values for coupling strength and extensive numerical simulations are included. In addition, for illustrative purposes, we show the effectiveness of network synchronization by means of experimental implementation of coupled nine electronics fireflies in different topologies.

Dynamic coupling in small-world outer synchronization of chaotic networks

2021 ◽  
Vol 423 ◽  
pp. 132928
Author(s):  
A. Arellano-Delgado ◽  
R.M. López-Gutiérrez ◽  
R. Méndez-Ramírez ◽  
L. Cardoza-Avendaño ◽  
C. Cruz-Hernández
Keyword(s):  
Small World ◽  
Dynamic Coupling ◽  
Outer Synchronization

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

Friction and Tribological Considerations for Nanometer Range Machining

2001 ◽  
Author(s):  
Som Chattopadhyay
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Local Deformation ◽  
Experimental Results ◽  
Precision Machining ◽  
Complex Motion ◽  
Positioning Accuracy ◽  
Nanometer Range ◽  
Motion Characteristic ◽  
Low Speeds

Abstract Positioning accuracy within the range of nanometers is required for high precision machining applications. The implementation of such a range is difficult through the slides because of (a) irregular nature of friction at the slider-guideway interface, and (b) complex motion characteristic at very low speeds. The complexity arises due to the local deformation at the interface prior to breakaway, which is known as microdynamics. In this work prior experimental results exhibiting microdynamics have been appraised, and mathematical model developed to understand this behavior.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

Design and Experimental Analysis of Novel Refractometer Based on Photoelectric Sensor Technology

2011 ◽  
Vol 383-390 ◽  
pp. 5211-5215
Author(s):  
Yin Lin Li ◽  
Zhong Hua Huang ◽  
Kai Bo Hu
Keyword(s):  
Mathematical Model ◽  
Experimental Analysis ◽  
Differential Method ◽  
Theoretical Solution ◽  
Experimental Results ◽  
Sensor Technology ◽  
Photoelectric Sensor ◽  
Better Than

A novel refractometer based on photoelectric sensor technology and differential method is proposed. Sensing principle and mathematical model are introduced; structure and key parameters of sensing probe are designed through detail calculation. Theoretical solution shows resolution reaches order of 10-5. Preliminary experiments verify the feasibility of the design, experimental results show stability error better than ±1.02×10-4, error caused by temperature is 6.65×10-6/°C.

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