NEW CONDITIONS FOR K- LIKE PROPERTIES OF ASYMPTOTICALLY STABLE SOLUTIONS FOR WEAKLY PERTURBED SYSTEMS FOR A CERTAIN CLASS OF NONLINEAR DIFFERENTIALS EQUATIONS | Journal of Applied Physical Science International
For a certain class of nonlinear differential equations, this work describes one broad method to the investigation of stable – like features of solutions for a weakly nonlinear system with tiny perturbing motions. The properties of the analysed equations include K- Stability, K- Unstable, and Asymptotically K- Stables. The method is based on a generalisation of the direct Lyapunov method mixed with nonlinear mechanics' asymptotic and averaging methods. In some cases, this strategy allows researchers to investigate classes of systems with a tiny parameter while making new, broader assumptions about the features of the researched systems' solutions. As a consequence of the research, the following conclusions were reached: K- stability for the system [1.3], K- unstable for the system [1.1], and Asymptotically K- stable for the system [1.1]. In the scenario where more than two reasons of the researched system attributes were established, my technique and results improved on [4.15] in the literature. Please see the link :- https://www.ikprress.org/index.php/JAPSI/article/view/6669 Keywords :- New conditions, K – stable, weakly perturbed, nonlinear equations.
A trade I took in $BABA. A trend reversal strategy on a daily support level I found As soon as the trading volume increased and the MACD oscillator signaled to me that there was weakness in the stock, I entered the trade and exited at the nearest resistance level.
[eTextBook] Asymptotic methods for relaxation oscillations and applications https://digsell.net/wp-content/uploads/2022/02/a6fe38ad2e2fec1a60889891d4b85141-d.jpg The book deals with the symptotic analysis of relaxation oscillations, which are nonlinear oscillations characterized by rapid change o...
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Akram, Tayyaba, Zeeshan Ali, Faranak Rabiei, Kamal Shah, and Poom Kumam. 2021. "A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel" Fractal and Fractional 5, no. 3: 85. https://doi.org/10.3390/fractalfract5030085
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Rapid Approximation of Weakly-Nonlinear Mode Parameters (October 2020)
Summary of Publication:
Modal processors and synthesizers require determining resonant frequencies and decay rates of a system. We introduce a simple, efficient, and flexible approach to compute these parameters when speed is of the essence, for example modeling a user’s sample folder in a realtime mobile synthesizer application. The approach compares DFT peaks in two impulse response windows at different points in time to obtain the modal frequencies and decay rates. The approach trades precision for speed, and should be considered an approximation. For a selection of samples across tonal/atonal instruments and reverb responses, we consider sensitivity to window choice and window size, and compare results to traditional modeling methods, which operate on the entire impulse response. We propose extensions of the algorithm to more than two windows, and to capture nonlinear, time-varying behavior such as the pitch dive after striking a tom drum at high velocity.
Forex Trading System Based on Detrend Price Oscillator
In this article we are going to explain in detail a trading system based on the technical indicatorIn this article we are going to explain in detail a trading system based on the Detrend Price Oscillator (DPO)It also uses other indicators to confirm DPO signals, in this case MACD and ADX. The ADX and its complements (-DI and +DI) represent a group of directional movement indicators and among other things measure the strength of the current trend. The combination of these three indicators produces a system with signals of greater reliability, which can be used to carry out medium-term operations in time frames of 60 minutes. As always, it is recommended to test this system on a demo account before using it for real money trading.
System configuration
Currency pairs: All.
1 candlestick/bar chart with a 1 hour time frame.
1 simple moving average of 3 periods.
1 simple moving average of 15 periods.
Detrend Price Oscillator (DPO) indicator set to 12.
The opening of buy and sell positions are based on the DPO crossing above/below the zero line. These signals are confirmed by the other indicators for greater reliability.
Long positions
The DPO must cross above the zero line.
The MACD line must be above the signal line.
In the ADX, the +DI must be above the –DI or at least it must be crossing above the –DI. This is not 100% necessary, but it is preferable.
Finally, the 3-period moving average must cross above the 15-period moving average in a period not to exceed three candlesticks, either before or after the DPO's bullish crossover.
The stop loss is placed below the 15-period moving average, at least 10 pips away, depending on the trader's risk tolerance.
Short positions
The DPO must cross below the zero line.
The MACD line must be below the signal line.
In the ADX, the +DI must be below the –DI or at least it must be crossing below the –DI. This is not 100% necessary, but it is preferable.
Finally, the 3-period moving average must cross below the 15-period moving average in a period not to exceed three candlesticks, either before or after the DPO's bullish crossover.
The stop loss is placed above the moving average of 15 periods, at a distance of at least 10 pips, depending on the risk tolerance of the trader.
System Example Charts
Buy signal example for the EUUSD pair In the example above we can see a good buy signal on the EUUSD. On the same candlestick, the DPO crosses above the zero line, the +DI crosses over the –DI, the 3-period moving average crosses the 15-period moving average, and the MACD has just moved above the signal line. In this case, we wait for the close of the candlestick and open a long position on the next candlestick to ensure the reliability of the moving average crossover. This is usually a good practice to avoid premature entry. As you can probably tell, there is another good buy signal which occurred shortly after the closing of the first position, but it is not included in this example to keep it simple.
Entry: 2629
Stop loss: 2601 (28 pips, that is 10 pips below the moving average of 15 pips)
Closing the position: 2751 (when the bearish crossover of the moving averages occurs)
Profit: 122 pips.
Example of a sell signal on the EUUSD pair In the image above we can see an excellent sell signal with this system. The reason for this statement is that each indicator shows a sell signal on the same candlestick simultaneously. We can see the DPO crossing the zero line, and at the same time the +DI crossed below the –DI and bearish crossover of the 3-period moving average and the 15-period moving average occurred, confirming the signal. The MACD was also below the signal line. Signals like this are the ones that have the highest chance of success. One thing we can notice is that prices temporarily pulled back almost to the exact 15 minute moving average, and then continued in the expected direction. This is something that happens more or less frequently.
Entry: 2338
Stop loss: 2368 (at a distance of 30 pips, i.e. 14 pips above the moving average of 15 pips)
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So I have a problem to solve which I struggle to do : ) It says - A nonlinear oscilator is described by the equation x double dotted + epsilon*(x dotted)^3+x=0, the initial values for the displacement and speed being x(0)=a and x dotted(0)=0. I have to solve the problem using the Lindstedt-Poincare method, deriving the first two terms of the asymptotic expansion of the solution. The problem is that I don't even know where to start : ) I ve been solving similar exercises but I m stuck at this one. I don't like to ask someone to help/ do something for me, but I really don't know how to do this problem, such that I'll be very thankful if you could help me here )
Expression for Frequency of Nonlinear oscillations?
I'm trying to fit a curve based on an empirical relation onto another, experimentally obtained curve. The experimentally obtained curve is the Displacement - Time plot of a damped pendulum in the nonlinear range, outside the small-angle approximation. The empirical relation ( X =A\cos(w*t\*)** ) where 'A' is a polynomial representing the profile of the curve, and 'w' is the frequency, which has a constant value throughout the response. The frequency of the pendulum evolves with amplitude (frequency increases as the oscillations die down, i.e, time period decreases), and so the plots look something like this. As you can see, the frequencies match during the first few oscillations but are out of phase during the next few oscillations and so on. Is there any way to accommodate an expression for 'w' such that it also increases with time? I can't use the Bernoulli power series either because that is a part of another solution. This is driving me nuts so any help would be appreciated!
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