Synchronization of Spatiotemporal Irregular Wave Propagation Via Boundary Coupling

Abstract Wave dynamics reflect a broad spectrum of natural phenomena and are often characterized by wave equation such as in the development of meta-devices used to steer wave propagation. Modeling synchronization of wave dynamics is critical in various applications such as in communications and neuroscience. In this paper, we study the synchronization problem for oscillations governed by wave equation with nonlinear (van der Pol type) boundary conditions through a single boundary coupling. The dynamics of the master system is self-excited and presents sensitive and rapid oscillations. With the only signal received at one end of the boundary, by constructing a mathematical model, we show the existence of a slave system that can be synchronized with the master system via the study of wave reflections on the boundary to recover the actual wave dynamics. The coupling gain, which represents the strength of the connection between the master system and the slave system, has been identified. The obtained result can be also viewed as an observer construction when the measurable output is only on the boundary. Numerical simulations are provided to demonstrate the effectiveness of the theoretical outcomes.

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Time Dependent Wave Propagation Modeling Using Finite Difference Scheme of 2D Wave Equation Based on Absorbing and Reflecting Boundaries

Journal of Applied Mathematics and Physics ◽

10.4236/jamp.2021.99148 ◽

2021 ◽

Vol 09 (09) ◽

pp. 2334-2344

Author(s):

M. Joni Alam ◽

W. Z. Loskor ◽

M. Mohiuddin

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Time Dependent ◽

Propagation Modeling ◽

Reflecting Boundaries ◽

Wave Propagation Modeling

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Brief review on PE method application to propagation channel modeling in sea environment

Open Engineering ◽

10.2478/s13531-011-0049-y ◽

2012 ◽

Vol 2 (1) ◽

Cited By ~ 16

Author(s):

Irina Sirkova

Keyword(s):

Wave Propagation ◽

Fourier Transform ◽

Parabolic Equation ◽

Initial Conditions ◽

Channel Modeling ◽

Radio Propagation ◽

Propagation Channel ◽

Tropospheric Propagation ◽

Propagation Modeling ◽

Wave Propagation Modeling

AbstractThis work provides an introduction to one of the most widely used advanced methods for wave propagation modeling, the Parabolic Equation (PE) method, with emphasis on its application to tropospheric radio propagation in coastal and maritime regions. The assumptions of the derivation, the advantages and drawbacks of the PE, the numerical methods for solving it, and the boundary and initial conditions for its application to the tropospheric propagation problem are briefly discussed. More details are given for the split-step Fourier-transform (SSF) solution of the PE. The environmental input to the PE, the methods for tropospheric refractivity profiling, their accuracy, limitations, and the average refractivity modeling are also summarized. The reported results illustrate the application of finite element (FE) based and SSF-based solutions of the PE for one of the most difficult to treat propagation mechanisms, yet of great significance for the performance of radars and communications links working in coastal and maritime zones — the tropospheric ducting mechanism. Recent achievements, some unresolved issues and ongoing developments related to further improvements of the PE method application to the propagation channel modeling in sea environment are highlighted.

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Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211000924 ◽

2021 ◽

pp. 014233122110009

Author(s):

Xin Meng ◽

Baoping Jiang ◽

Cunchen Gao

Keyword(s):

Fractional Order ◽

Sliding Mode ◽

Coupled Systems ◽

Projective Synchronization ◽

Slave System ◽

Complete Synchronization ◽

Synchronization Problem ◽

Strong Connectedness ◽

Master System ◽

Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

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