Fractional-order Circuit Research Articles

Dynamics and Synchronization of Memristor-Based Fractional-Order System

A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed through the approximation method of fractional order operator. In addition, it clearly describes the relationships between the impedance variation of the memristor and the varying mobility of the doped region of the memristor in different circuit parameters. Finally, a periodic memristor-based system driven by another chaotic memristor-based fractional order system is synchronized to chaotic state via the linear error feedback technique.

Theory of Fractional Order Elements Based Impedance Matching Networks

Fractional order circuit elements (inductors and capacitors) based impedance matching networks are introduced for the first time. In comparison to the conventional integer based L-type matching networks, fractional matching networks are much simpler and versatile. Any complex load can be matched utilizing a single series fractional element, which generally requires two elements for matching in the conventional approach. It is shown that all the Smith chart circles (resistance and reactance) are actually pairs of completely identical circles. They appear to be single for the conventional integer order case, where the identical circles completely overlap each other. The concept is supported by design equations and impedance matching examples.

Fractional Smith Chart Theory

For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach.

Circuit implementation of a new hyperchaos in fractional-order system

This paper introduces a new four-dimensional (4D) hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincaré mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.

A hyperchaotic system and its fractional order circuit simulation

A hyperchaotic system and its fractional order circuit simulation