The problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron–Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features. As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment.

A tensor approach to higher order expectations of quantized chaotic trajectories - part I: general theory and specialization to piecewise affine markov systems / Rovatti, R.; Mazzini, G.; Setti, G.. - In: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I. FUNDAMENTAL THEORY AND APPLICATIONS. - ISSN 1057-7122. - STAMPA. - 47:11(2000), pp. 1571-1583. [10.1109/81.895325]

A tensor approach to higher order expectations of quantized chaotic trajectories - part I: general theory and specialization to piecewise affine markov systems

SETTI G.
2000

Abstract

The problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron–Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features. As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2696635
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