McDonald, Andre MVan Wyk, A2019-03-272019-03-272017-12McDonald. A.M. and Van Wyk, A. 2017. Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem. Proceedings of the Asia-Pacific Signal and Information Processing Association Summit and Conference 2017, Kuala Lumpur, Malaysia, 12-15 December 2017http://apsipa2017.org/list-accepted-papers/http://hdl.handle.net/10204/10862Conference paper presented at the Asia-Pacific Signal and Information Processing Association Summit and Conference 2017, Kuala Lumpur, Malaysia, 12-15 December 2017This paper presents a novel technique for constructing semi–Markov ergodic maps that harnesses a new solution of the inverse eigenvalue problem for 3–by–3 doubly stochastic matrices. The proposed solution facilitates the selection of the spectral characteristics of the trajectories generated by these ergodic maps through the selection of appropriate eigenvalues for the Frobenius–Perron matrices associated with the maps. It is proved that the proposed solution is able to realise all possible eigenvalue triples for the matrices of interest, thereby providing greater freedom in selecting the power spectral density than existing techniques. The novel technique is demonstrated by constructing several semi–Markov ergodic maps with distinct power spectra. It is concluded that the flexibility and versatility of the technique holds potential for the purpose of system modelling in various contexts.enInverse eigenvalue problemInverse Frobenius Perron problemDynamical systemChaosConference PresentationMcDonald, A. M., & Van Wyk, A. (2017). Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem. http://hdl.handle.net/10204/10862McDonald, Andre M, and A Van Wyk. "Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem." (2017): http://hdl.handle.net/10204/10862McDonald AM, Van Wyk A, Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem; 2017. http://hdl.handle.net/10204/10862 .TY - Conference Presentation AU - McDonald, Andre M AU - Van Wyk, A AB - This paper presents a novel technique for constructing semi–Markov ergodic maps that harnesses a new solution of the inverse eigenvalue problem for 3–by–3 doubly stochastic matrices. The proposed solution facilitates the selection of the spectral characteristics of the trajectories generated by these ergodic maps through the selection of appropriate eigenvalues for the Frobenius–Perron matrices associated with the maps. It is proved that the proposed solution is able to realise all possible eigenvalue triples for the matrices of interest, thereby providing greater freedom in selecting the power spectral density than existing techniques. The novel technique is demonstrated by constructing several semi–Markov ergodic maps with distinct power spectra. It is concluded that the flexibility and versatility of the technique holds potential for the purpose of system modelling in various contexts. DA - 2017-12 DB - ResearchSpace DP - CSIR KW - Inverse eigenvalue problem KW - Inverse Frobenius Perron problem KW - Dynamical system KW - Chaos LK - https://researchspace.csir.co.za PY - 2017 T1 - Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem TI - Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem UR - http://hdl.handle.net/10204/10862 ER -