scholarly journals Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Elena Adomaitienė ◽  
Skaidra Bumelienė ◽  
Gytis Mykolaitis ◽  
Arūnas Tamaševičius
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
Mean Field ◽  
Electrical Circuit ◽  
Voltage Source ◽  
Dc Voltage

A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

Model Based Temperature Control in RTP Yielding ±0.1 °C accuracy on A 1000 °C, 2 second, 100 °C/s Spike Anneal

1998 ◽  
Vol 525 ◽  
Author(s):  
Peter Vandenabeele ◽  
Wayne Renken
Keyword(s):  
Differential Equations ◽  
Temperature Control ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
System Response ◽  
Model Based Control ◽  
First Order ◽  
Model Based ◽  
Measured System ◽  
Spike Anneal

ABSTRACTA Model Based Control method is presented for accurate control of RTP systems. The model uses 4 states: lamp filament temperature, wafer temperature, quartz temperature and TC temperature. A set of 4 first order, nonlinear differential equations describes the model. Feedback is achieved by updating the model, based on a comparison between actual (measured) system response and modeled system response.

A Random Stimulation Source for Evaluating MEMS Devices using an Exact Solvable Chaotic Oscillator

2015 ◽  
Vol 2015 (DPC) ◽  
pp. 001594-001625 ◽  
Author(s):  
Aubrey N. Beal ◽  
Robert N. Dean
Keyword(s):  
Differential Equations ◽  
Flip Chip ◽  
Chaotic Systems ◽  
Nonlinear Differential Equations ◽  
Hardware Verification ◽  
Voltage Source ◽  
Chaotic Oscillator ◽  
Mems Devices ◽  
Wide Bandwidth ◽  
Forcing Function

MEMS devices are nearly ubiquitous, with applications ranging from automobiles to toys, medical equipment to missiles, and cell phones to industrial equipment. At the microscale, fabrication tolerances are significantly less precise than at the scale of traditional machining techniques. This can result in significant differences in the operating characteristics between otherwise identical MEMS devices. A wide bandwidth random excitation source is ideal for evaluating these components, whether used as the forcing function for an electromechanical shaker employed to measure transmissibility, or as a voltage source to evaluate actuator structure resonances and instabilities. An electronic chaotic oscillator provides an ideal wide bandwidth voltage source which is provably random from first principles and may be simply integrated for the aforementioned MEMS testing. This type of system is easily integrated through standard Si MEMS processes and readily lends itself to application as a built-in-self test (BIST) component. These systems guarantee uniform frequency content from D.C. up to 100kHz due to their characteristically random behavior and serve as a strong candidate for providing uniform spectral density to a device under test. The proposed system is a simple, electronic circuit that creates a random, wideband excitation voltage for observing characteristics of MEMS devices. This functionality is achieved by the analog, digital or mixed signal computation of nonlinear differential equations that describe various exactly solvable chaotic systems. By creating Si microsystems which perform these computations, these test sources may be readily fabricated as integrated BIST components for MEMS devices or fabricated separately and integrated by flip chip assembly techniques. Furthermore, by considering the iterated map of this particular category of stimulation source, a direct and easy measurement of the stimulation entropy may be monitored and corrected. This work begins as a theoretical treatment involving the Nonlinear Dynamics of these types of systems including chaotic systems which permit closed form solutions. These systems are described classically through nonlinear differential equations and intuitively through iterated maps. These techniques reveal inherent methods for entropy measurement in these sources which may be implemented and controlled easily using electronic circuits. Subsequently, the simulation, circuit design methodology, circuit simulation, fabrication, testing and hardware verification of these wideband chaotic sources is presented. The development of this work delineates simple, wideband electronic testing circuits which may be fully integrated with MEMS devices using standard Si MEMS processes. The resulting microsystem may be used as the forcing function when measuring transmissibility of MEMS devices, or as a BIST element to evaluate MEMS microstructure characteristics through direct microelectronic fabrication or flip chip integration.

Haar wavelet based numerical solution of nonlinear differential equations arising in fluid dynamics

2016 ◽  
Vol 05 (02) ◽  
pp. 1650010 ◽  
Author(s):  
S. C. Shiralashetti ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Fluid Dynamics ◽  
Differential Equations ◽  
Error Analysis ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Elastohydrodynamic Lubrication ◽  
Haar Wavelet ◽  
Nonlinear Boundary Value Problems

In this paper, we obtained the Haar wavelet-based numerical solution of the nonlinear differential equations arising in fluid dynamics, i.e., electrohydrodynamic flow, elastohydrodynamic lubrication and nonlinear boundary value problems. Error analysis is observed, it shows that the Haar wavelet-based results give better accuracy than the existing methods, which is justified through illustrative examples.

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