Interval Perturbed Motion of Modified Discrete-Time Mackey-Glass System

Our paper is devoted to the design of a novel chaotic oscillator. Our design uses a well-known Mackey-Glass system. We consider the above-mentioned chaotic system in the discrete-time domain and assume that its parameters can change at some intervals. This assumption allows us to write down an interval model Mackey-Glass system. This model can be used to define the amplitude of chaotic oscillations in the interval boundaries that correspond above-mentioned intervals of system parameters. At the same time, system nonlinearity makes it quite hard to analyze system dynamics and perform system transformations. That is why we define piecewise linear boundaries for the state space domain where the system nonlinearity is defined. These piecewise linear functions give us the possibility to rewrite the nonlinear interval Mackey-Glass equation into linear-like equations and formulate some requirements for the generalized infinite-dimension system with chaotic dynamics. One can use the above-mentioned interval equation to define system average motion and motions which are caused by fluctuations of system parameters. The last one we call a system perturbed motion equation and use known system equations to transform it into a form that does not depend on average system motion. The benefits of our approach are proven by simulation results which can be performed by using various MCU/FPGA devices to implement the proposed chaotic oscillator.