In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with nth-order ordinary differential equations where n is 4 or up to. Hyperjerk systems have been investigated in literature in the last decade. This paper consists of numerical studies and experimental realization on FPAA for fourth-order hyperjerk system with exponential nonlinear function.

Some chaotic systems can be realized with different nonlinear functions. These systems consist of a fixed main system block and a changeable nonlinear function block. Studying with these generalized systems is very useful from the educational point of view including general modeling and design issues of chaotic systems. SIMULINK, a graphical programming tool, offers a very good environment for dynamic modeling of such generalized chaotic systems. This paper presents generalized two chaotic systems, which can be utilized in chaotic system modeling for engineering applications and the use of SIMULINK in dynamical modeling and simulation of these generalized systems which can be realized with multiple nonlinear functions. The proposed models have been integrated into undergraduate nonlinear circuits and systems course at Erciyes University, Kayseri, Turkey. ß

Purpose The purpose of this study is to make artificial neural network (ANN)-based prediction about thrust using the flight control parameters of aircrafts. Design/methodology/approach In today’s transportation, airplanes have an important place because of their safety, quality and speed. One of the most important parameters affecting the secure flying of aircrafts is the thrust value of aircraft engines. Determining the optimum thrust value should be investigated. If thrust value is less than optimum level, the flight safety runs a risk. Otherwise, fuel consumption goes high and some unwanted vibrations occur that cause uncomfortable flight. In this study, multi-layer perceptron ANNs, which are one of the intelligent optimization methods and frequently used in the literature, are preferred to predict the optimum thrust value during take-off, cruise and landing. The actual flight data, which is taken from the black box of an Airbus A319 aircraft, is used to train ANN models using back propagation algorithms. Velocity, altitude and ambient temperature values of the aircraft are selected as inputs and the thrust value is selected as output. During the training process of ANN, eight different training algorithms with different structures are used to figure out optimum ANN model with minimum error. Findings Different ANN models were trained using eight different training algorithms. The ANN model with minimum error has multi-layer perceptron structure, which is trained using Levenberg–Marquardt (LM) algorithm. Research limitations/implications To obtain the ANN structure with minimum error training, process takes more than a day depending on the capacity of a computer for LM training algorithm. But after training process, the trained ANN model produces sufficient output in a few milliseconds. Practical implications Totally 15,670 input-output data sets are obtained from an Airbus A319 aircraft. 12,889 of them are used as training data and the rest of the data sets, selected randomly are used as test data. Test data sets are never used in training phase, and the obtained results show that the ANN model successfully predicts thrust value using unseen input data. Social implications The ANN could be used as an alternative method to predict other flight control parameters of aircrafts. Originality/value To the best of authors’ knowledge, this study is the first example in literature to predict the thrust value of the aircraft using ANN.

Chua's circuit is very suitable as a programmable chaos generator because of its robust nonlinearity. In addition to exhibiting a rich variety of bifurcation and chaos phenomenon, this circuit can be modeled and realized with a fixed main system block and many different nonlinear function blocks such as piecewise-linear function, cubic-like function, piecewise-quadratic function and other trigonometric functions. This paper presents a FPAA (Field Programmable Analog Array) based programmable implementation of Chua's circuit. Nonlinear function blocks used in Chua's circuit are modeled with an FPAA and hence a model can be rapidly changed for realization of other nonlinear functions. In this study, four FPAA-based reconfigurable implementations of Chua's circuit have been realized. Experimental results agree with numerical simulation and results obtained from discrete electronic implementations of Chua's circuit.

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