A brief note on possible detection of physiological singularities in respiratory dynamics by recurrence quantification analysis of lung sounds

Chaos, Solitons and Fractals

Volumn 21, Issue 4, 2004, Pages 869-877

  Conte, Elio ^a   Vena, Antonio ^a   Federici, Antonio ^a   Giuliani, Rocco ^a   Zbilut, Joseph P ^b  

^a UNIVERSITY OF BARI   (Italy)

^b RUSH MEDICAL COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; ACOUSTIC SIGNAL PROCESSING; CHAOS THEORY; FEEDBACK CONTROL; LYAPUNOV METHODS; PATHOLOGY; PHYSIOLOGY;

LIPSCHITZ CONDITIONS; LUNG SOUNDS; RECURRENCE QUANTIFICATION ANALYSIS;

RESPIRATORY MECHANICS;

EID: 1542380064     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2003.12.098     Document Type: Article

References (25)

1. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
2. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
3. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
4. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
5. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
6. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
7. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
8. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
9. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
10. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
11. The relevance of singularities in physiological systems was prospected for the first time by J.P. Zbilut in collaboration with A. Hubler and C.L. Webber at the Conference Fluctuations and Order: the New Synthesis (Conference sponsored by the Center for Nonlinear Studies, Loas Alamos National Laboratories and the Santa Fe Institute, Santa Fe, New Mexico, Sept. 9-12, 1993) by a contribution entitled Nondeterministic Equations of Motion as a Result of Noise Perturbation. The paper was subsequently published by J.P. Zbilut, A. Hubler, C.L.Webber, Physiological singularities modeled by nondeterministic equations of motion and the effect of noise. In: M. Millonas edition, Fluctuations and Order: The New Synthesis. New York: Springer Verlag; 1996. p. 397-417. Other papers may be quoted here: Zbilut JP, Zak M, Webber CL. Nondeterministic chaos approach to neural intelligence. In: Intelligent Engineering Systems Through Artificial Neural Networks, vol. 4. New York: ASME Press; 1994. p. 819-24 Zbilut J.P., Zak M., Meyers E.R. A terminal dynamics model of the heartbeat. Biol. Cybernet. 75:1996;277-280 Zak M., Zbilut J.P., Meyers E.R. From instability to intelligence complexity and predictability in nonlinear dynamics, Lecture Notes in Physics: New Series m49. 1997;Springer-Verlag, Berlin Heidelberg, New York, Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zak M. The problem of irreversibility in newtonian dynamics. Int. J. Theoret. Phys. 31(2): 1992;333-342 Zak M. Terminal chaos for information processing in neurodynamics. Biol. Cybernet. 64:1991;343-351 Zak M. Non-Lipschitzian dynamics for neural net modelling. Appl. Math. Lett. 2(1):1989;69-74 Zak M. Dynamical simulation of probabilities. Chaos, Solitons & Fractals. 5:1997;793-804 Zak M. Non-Lipschitz approach to quantum mechanics. Chaos, Solitons & Fractals. 9:1998;1183-1198 Giuliani A., LoGiuduce P., Mancini A.M., Quatrini G., Pacifici L., Webber C.L., et al. A Markovian formalization of heart rate dynamics evinces a quantum like hypothesis. Biol. Cybernet. 7:1996;4181-4187.
12. Somjen G.G. The missing error signal-regulation beyond negative feedback. News Physiol. Sci. 7:1992;184-185.
13. Conte E, Federici A, Zbilut JP. A brief note on discrete non deterministic dynamics in compartment theory of biological observables. Chaos, Solitons & Fractals, submitted for publication.
14. Zbilut J.P., Zak M., Webber C.L. Physiological singularities in respiratory and cardiac dynamics. Chaos, Solitons & Fractals. 5:1995;1509-1516.
15. von Euler C. Brain stem mechanism for generation and control of breathing patterns. In: Handbook of Physiology. The Respiratory System. Control of Breathing, Am. Physiol. Soc., Bethesda, MD, Sect. 3, vol. II, 1986. p. 1-67 (Chapter 1).
16. Eldrige F.L. Phase resetting of respiratory rhythm. Haken H., Koepchen H.P. Rhythms in Physiological Systems. 1991;Springer, New York.
17. Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zbilut J.P., Zaldivar-Comenges J.M., Strozzi F. Recurrence quantification based-Lyapunov exponents for monitoring divergence in experimental data. Phys. Lett. A. 297:2002;173-181.
18. Zbilut J.P., Dixon D.D., Zak M. Detecting singularities of piecewise deterministic (terminal) dynamics in experimental data. Phys. Lett. A304:2002;95-101 Zbilut J.P., Zaldivar-Comenges J.M., Strozzi F. Recurrence quantification based-Lyapunov exponents for monitoring divergence in experimental data. Phys. Lett. A. 297:2002;173-181.
19. Rossi M., Sovijarvi A.R.A., Piirila P., Vannuccini L., Dalmasso F., Vanderschoot J. Environmental and subject conditions and breathing manoeuvres for respiratory sound recordings. Eur. Respirat. Rev. 10(77):2000;611-615.
20. Webber C.L., Zbilut J.P. Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2):1994;965-973.
21. Eckmann J.P., Kamphorst S.O., Ruelle D. Recurrence plots of dynamical systems. Europhys. Lett. 4:1987;973-977.
22. Grassberger P., Schreiber T., Schaffrath C. Nonlinear time sequence analysis. Int. J. Bifurcat. Chaos. 1:1991;521-547.
23. Schreiber T. Interdisciplinary application of non-linear time series methods. Phys. Rep. 308:1999;1-64.
24. Zbilut J.P., Thomasson N., Webber C.L. Recurrence quantification analysis as a tool for nonlinear exploration of nonstationarity cardiac signals. Med. Engng. Phys. 9:2001;1-8 Schockley K., Butwill M., Zbilut J.P., Webber C.L. Cross recurrence quantification of coupled oscillators. Phys. Lett. A. 305:2002;59-69.
25. Zbilut J.P., Thomasson N., Webber C.L. Recurrence quantification analysis as a tool for nonlinear exploration of nonstationarity cardiac signals. Med. Engng. Phys. 9:2001;1-8 Schockley K., Butwill M., Zbilut J.P., Webber C.L. Cross recurrence quantification of coupled oscillators. Phys. Lett. A. 305:2002;59-69.