Design of a Web Interface for Fractional Chaotic Systems

Abstract

There exists a great number of work related to chaotic systems investigated by many researchers, especially about Lorenz chaotic system. If the order of differentiation of variables are fractional, the systems are called fractional chaotic systems. In this work a webbased interface is designed for fractional composition of five different chaotic systems. The interface takes initial and fractional differentiation values and yields output signals and phase portraits. The paper first introduces design tools and then provides results obtained throughout the experiments.

Review, Design, Optimization and Stability Analysis of Fractional-Order PID Controller

“…Short memo ry principle means taking into account the function behavior only in the "recent past". The results obtained by these methods are more reliab le than those determined using the frequencybased approximat ion [10]. This would then result in approximating (22) by truncating backwards summation, only taking into account times on the interval   [66] introduce an adaptive timestep method for co mputing the contribution of the memo ry effect associated with the h istory of a system, where fractional methods must be taken into account.…”

“…An alternative way is the study of the transfer function of the system [23]. There are even some attempts to develop polynomial techniques, either Routh or Jury type, to analy ze their stability [10], [68,69]. Saeed Balochian et al [70] present the stabilization problem of a LTI-Fo switched system by a single Lyapunov function whose derivative is negative and bounded by a quadratic function within the activation of each subsystem.…”

“…Its applicability to science and engineering can be considered as an emerging new topic. It includes some areas, such as biology and chemical engineering (irrigation canal control [2], low pressure flowing water network [3], networked control system [4]), control and simulat ion of photovoltaic-wind energy systems [5,6], hydraulic turbine regulation [7], flight control [8], fractional-order chaotic systems modeling and control [9,10], Modeling of Econo mic Order Quantity [11], control of a servo systems [12,13], realization of higher-order filters [14], robotic control [15], astronomy [16], .. etc.…”

“…For nu merical calcu lation of fract ionalorder derivative, we can use the relation (2) derived fro m the GL definition. Th is approach is based on the fact that for a wide class of functions, GL (2), RL (3) and Caputo"s (4) are equivalent [10]. The fract ional-order derivative and integral can also be defined in the transformation-do main.…”

“…It is noted that some MATLAB-tools of the fractional-order dynamic system modeling, control and filtering can be found in [39,40]. Nu merical methods for simu lating and discretization fractional-order systems are given in detail in [10] and [41].…”