Öz
Doğrusal olmayan dinamik sistemler ile ilgili çalışmalar günümüzde bilimsel çalışmaların merkezinde yer almaktadır. Fizik bilimi, biyo-sistemler, yeni teknolojiler ve iktisat gibi bir çok bilim disiplini doğrusal olmayan dinamik sistemlerin davranışlarına göre modeller oluşturmakta ve bu konularda çalışmalar yapmaktadırlar. Bu nedenle bu yazıda iyi bilinen birkaç doğrusal olmayan dinamik sistem örnek verilerek bu sistemlerin nasıl incelendiği üzerinde durulacaktır. Bunun yanında fiziksel sistemlerin davranışı veya bilgi teorisinde önemli bir yere sahip olan çeşitli entropi tanımları tartışılacaktır. Ayrıca doğrusal olmayan sistemlerle doğrudan ilgili olan kompleksite biliminin genel kavramları üzerinde de kısaca durulacaktır.
Anahtar Kelimeler
Kaynakça
- Allegrini, P., Giuntoli, M., Grigolini, P., & West, B. J. (2004). From knowledge, knowability and the search for objective randomness to a new vision of complexity. Chaos, Solitons & Fractals, 20(1), 11-32. https://doi.org/10.1016/S0960-0779(03)00424-7
- Badii, R., & Politi, A. (1997). Complexity. Cambridge University Press. https://doi.org/10.1017/CBO9780511524691
- Dorfman, J. R. (1999). An introduction to chaos in nonequilibrium statistical mechanics. Cambridge University Press. https://doi.org/10.1017/CBO9780511628870
- Enns, R. H., & McGuire, G. C. (1997). Nonlinear physics with Maple for scientists and engineers. Birkhauser.
- Eren, E., & Şahin, S. (Ed.). (2017). Kompleksite ve İktisat. Efil Yayınevi.
- Faye, J. (2019). Copenhagen interpretation of quantum mechanics. E. N. Zalta (Ed.), The Stanford Encyclopaedia of Philosophy içinde (Winter 2019 ed.). https://plato.stanford.edu/entries/qm-copenhagen
- Koschmieder, E. L. (1974). Advances in Chemical Physics. Wiley. https://doi.org/dqtt5k
- Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130-141. https://doi.org/fwwt5q
- Marion, J. B., & Thornton, S. T. (1995). Classical Dynamics of Particles and Systems. Saunders College Publishing.
- Masi, M. (2005). A step beyond Tsallis and Rényi entropies. Physics Letters A, 338(3-5), 217-224. https://doi.org/10.1016/j.physleta.2005.01.094
- Neff, R. B. & Tillman, L. (1975). Three new pocket calculators: Less costly, more powerful. Hewlett-Packard Journal, 27(3), 2-7. https://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1975-11.pdf
- Peterson, I. (1993). Newton's clock: Chaos in the solar system. Freeman.
- Scott, A. C., Chu, F. Y. F., & McLaughlin, D. W. (1973). The soliton: A new concept in applied science. Proceedings of the IEEE, 61(10), 1443-1483. https://doi.org/fcvksh
- Thom, R. (1989). Structural stability and morphogenesis. Westview Press. https://doi.org/fsk2
- Van der Pol, B. (1926). LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 978-992. https://doi.org/10.1080/14786442608564127
- Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285-317. https://doi.org/10.1016/0167-2789(85)90011-9
Öz
Studies on the nonlinear dynamic systems are at the centre of scientific studies today. Many scientific disciplines such as physics, bio-systems, new technologies and economics create models according to the behaviour of nonlinear dynamical systems and work on these subjects. Therefore, this article will focus on how these systems are studied by giving well-known a few examples of nonlinear dynamical systems. Also, the various definitions of entropy, which has an important place in the behaviour of physical systems or information theory, will be discussed. In addition, general concepts of the complexity science that are directly related to nonlinear systems will be briefly emphasized.
Anahtar Kelimeler
Kaynakça
- Allegrini, P., Giuntoli, M., Grigolini, P., & West, B. J. (2004). From knowledge, knowability and the search for objective randomness to a new vision of complexity. Chaos, Solitons & Fractals, 20(1), 11-32. https://doi.org/10.1016/S0960-0779(03)00424-7
- Badii, R., & Politi, A. (1997). Complexity. Cambridge University Press. https://doi.org/10.1017/CBO9780511524691
- Dorfman, J. R. (1999). An introduction to chaos in nonequilibrium statistical mechanics. Cambridge University Press. https://doi.org/10.1017/CBO9780511628870
- Enns, R. H., & McGuire, G. C. (1997). Nonlinear physics with Maple for scientists and engineers. Birkhauser.
- Eren, E., & Şahin, S. (Ed.). (2017). Kompleksite ve İktisat. Efil Yayınevi.
- Faye, J. (2019). Copenhagen interpretation of quantum mechanics. E. N. Zalta (Ed.), The Stanford Encyclopaedia of Philosophy içinde (Winter 2019 ed.). https://plato.stanford.edu/entries/qm-copenhagen
- Koschmieder, E. L. (1974). Advances in Chemical Physics. Wiley. https://doi.org/dqtt5k
- Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130-141. https://doi.org/fwwt5q
- Marion, J. B., & Thornton, S. T. (1995). Classical Dynamics of Particles and Systems. Saunders College Publishing.
- Masi, M. (2005). A step beyond Tsallis and Rényi entropies. Physics Letters A, 338(3-5), 217-224. https://doi.org/10.1016/j.physleta.2005.01.094
- Neff, R. B. & Tillman, L. (1975). Three new pocket calculators: Less costly, more powerful. Hewlett-Packard Journal, 27(3), 2-7. https://www.hpl.hp.com/hpjournal/pdfs/IssuePDFs/1975-11.pdf
- Peterson, I. (1993). Newton's clock: Chaos in the solar system. Freeman.
- Scott, A. C., Chu, F. Y. F., & McLaughlin, D. W. (1973). The soliton: A new concept in applied science. Proceedings of the IEEE, 61(10), 1443-1483. https://doi.org/fcvksh
- Thom, R. (1989). Structural stability and morphogenesis. Westview Press. https://doi.org/fsk2
- Van der Pol, B. (1926). LXXXVIII. On “relaxation-oscillations”. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 978-992. https://doi.org/10.1080/14786442608564127
- Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285-317. https://doi.org/10.1016/0167-2789(85)90011-9
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2020 |