Cite this article as:

Kuznetsov S. P. From Anosov’s Dynamics on a Surface of Negative Curvature to Electronic Generator of Robust Chaos. Izvestiya of Saratov University. New series. Series Physics, 2016, vol. 16, iss. 3, pp. 131-144. DOI:

517.9: 514.853: 621.373

From Anosov’s Dynamics on a Surface of Negative Curvature to Electronic Generator of Robust Chaos


Background and Objectives: Systems with hyperbolic chaos should be of preferable interest due to structural stability (roughness) that implies insensitivity to variation of parameters, manufacturing imperfections, interferences, etc. However, until recently, exclusively formal mathematical examples of this kind of dynamical behavior were known. It makes sense to turn to purposeful constructing the systems with hyperbolic dynamics appealing to tools of physics and electronics. Materials and Methods: Departing from a formal example of hyperbolic dynamics, that is a classical problem of geodesic flow on a surface of negative curvature, the idea is to modify the setup it in such way that the dynamical equations become appropriate to be associated with an electronic circuit hoping that due to the roughness the hyperbolic dynamics will survive this transformation. Results: The electronic scheme is elaborated and the dynamical equations are derived. Numerical integration of the equations and simulation of the electronic circuit using the software product NI Multisim supplemented with appropriate processing of the data obtained indicate correspondence of the observed dynamics with those for the geodesic flow. So, the system operates as a generator of robust chaos, at least in some wide range of parameters, and the produced signal has rather good spectral properties, without pronounced peaks and dips in the power spectral density distribution. Conclusion: Doe to roughness as the mathematically proven attribute of hyperbolic dynamics, the systems of this class seem preferable for practical applications of chaos. Although the circuit considered in the article operates at rather low frequencies (kilohertz), it seems possible to implement similar devices at high frequencies as well.


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