Two-Dimensional Hyperchaotic Map for Chaotic Oscillations

This manuscript explores a two-dimensional hyperchaotic map for generating chaotic oscillations. Hyperchaotic maps are finding increasing applications in various scientific and technological fields due to the unique properties of their generated oscillations. The studied map, based on two interconnected piecewise-linear functions, is one of the simplest for generating oscillations with a predetermined distribution of values across a continuous parameter space. This simplicity allows for wide applicability in various contexts. The paper presents simulation results demonstrating control over the parameters of the dynamic modes. Building upon these modeling results, a two-dimensional hyperchaotic system is implemented using an electric circuit. The chosen map is attractive due to its inherent simplicity and ease of parameter control. By adjusting these parameters, the distribution of the generated signal's values can be manipulated. The circuit consists of two symmetrical sections connected via feedback loops, employing four amplifiers with variable gain. The gain values act as the circuit's implementation of the control parameters. Chaotic oscillations are generated by applying a delayed clock signal from an external square wave generator to circuit elements. The obtained experimental results exhibit excellent agreement with the simulation data.