Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 11 Sayı: 3, 1887 - 1895, 01.09.2021
https://doi.org/10.21597/jist.804591

Öz

Kaynakça

  • Boshan, C, Jiejie, C, 2012. Bifurcation and chaotic behavior of a discrete singular biological economic system. Applied Mathematics and Computation 219, 5: 2371-2386.
  • Chen Q, Wang J, Yang S, Qin Y., Deng B., and Wei X, 2017. A real-time FPGA implementation of a biologically inspired central pattern generator network, Neurocomputing, 244, 63–80.
  • Elabbasy E M, Elsadany A A, and Zhang Y, 2014. Bifurcation analysis and chaos in a discrete reduced lorenz system. Applied Mathematics and Computation 228(2014), 184–194.
  • Ghaziani R K, Goverts K, Sonck C, 2012. Resonance and bifurcation a discrete time predator-prey system with Holling functional response. Nonlinear Analysis Real World Applications 13 (2012), 1451–1465.
  • Gleria IM, Figueiredo A, Rocha Filho, T M, 2001. Stability Properties of a General Class of Nonlinear Dynamical Systems. J.Phys A: Math. Gen. 34 3561-3575.
  • Goel NS, Maitra SC, and Montroll EW, 1971. On the Voltera and other nonlinear models of interacting populations. Rev. Modern Phys. 43, 231-276.
  • Gomar S, and Ahmadi A, 2014. Digital Multiplierless Implementation of Biological Adaptive-Exponential Neuron Model, IEEE Trans. Circuits Syst. I Regul. Pap., 61(4), 1206–1219.
  • He X, Liao M. & Xu C, 2011. Stability and Hopf Bifurcation analysis for a Lotka- Volterra predator-prey models with two delays, Int. J. Appl. Math. Comput., 21(1), 97- 107.
  • Kermack W O, and Mckendrick A G, 1927. A contribution to the mathematical theory of epidemics, Proceeding of Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700-72.
  • Kerner E H, 1957. The bulletin of mathematical biophysics. 19 (1957), 121.
  • Kimura M and Weiss G H, 1964. The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics 49 (1964), 561-576.
  • Korkmaz Tan R, and Bora Ş, 2019. Adaptive parameter tuning for agent-based modeling and simulation. Simulation: Transactions of the Society for Modeling and Simulation International, 95(9) 771-796.
  • Lotka A J, 1926. Elements of physical biology. Science Progress in the Twentieth Century, 21(82): 341-343.
  • Scheiner ER, 1996. Invitation to Dynamical Systems, The John Hopkins University Press, Washington, D.C.
  • Volterra V, 1978. Variazioni et fluttuazioni del numero d’individui in specie animali conviventi, Scudo ve Ziegler (Trans.), R. Comitato Talassografico Memoria, 6 (2), 31-113p.
  • Yener SC, Barbaros C, Mutlu R and Karakulak E, 2017. Implementation of Microcontroller-Based Memristive Chaotic Circuit, Acta Phys. Pol. A, 132(3), 1058–1061.
  • Yener ŞÇ, Barbaros C, Mutlu R and Karakulak E, 2018. Design of a Microcontroller-Based Chaotic Circuit of Lorenz Equations, in International Conference on Science and Technology ICONST 2018 5-9 September 2018 Prizren - KOSOVO, pp. 612–615.
  • Yener ŞÇ, Mutlu R, 2018. A Microcontroller-Based ECG Signal Generator Design Utilizing Microcontroller PWM Output and Experimental ECG Data, The Scientific Meeting on Electrical-Electronics Biomedical Engineering and Computer Science in 2018 (EBBT’2018) (18.04.2018-19.04.2018).
  • Yener SC, Mutlu R, 2019. - A Microcontroller Implementation Of Hindmarsh- Rose Neuron Model-Based Biological Central Pattern Generator, 1st International Informatics and Software Engineering Conference (UBMYK), 6-7 November 2019, Ankara.
  • Zhang G, Yi S and Boshan C, 2014. Bifurcation analysis in a discrete differential-algebraic predator-prey system. International Journal of Bifucation and Chaos, 38 (2014), 4559–4048.

STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations

Yıl 2021, Cilt: 11 Sayı: 3, 1887 - 1895, 01.09.2021
https://doi.org/10.21597/jist.804591

Öz

Lotka-Volterra equations are commonly used in prey-predator population studies. Simulation programs are commonly used to produce solutions of Lotka-Volterra equations and to examine their initial value dependendence. In literature, chaotic waveform generators, ECG and EEG generators have been made and used for research and education. To the best of our knowledge, such an electrical circuit to produce the Lotka-Volterra waveforms does not exist. Such a circuit can be made using either analog or digital circuit components. However, such a device may be used for education in classroom and also to prove concepts by population researchers. In this study, implementation and experimental verification of the microcontroller-based circuit which solves LotkaVolterra equations in real time and produces its waveforms are presented. Euler method is used to solve the equation system in discrete time. Presented design has been implemented using an STM32F429 Discovery Board, two DACs and four opamps. The microcontroller sends the signals to the outputs of the circuit using digital-to-analog converters and opamps. The waveforms acquired experimentally from the implemented circuit outputs matches well with those obtained from numerical simulations.

Kaynakça

  • Boshan, C, Jiejie, C, 2012. Bifurcation and chaotic behavior of a discrete singular biological economic system. Applied Mathematics and Computation 219, 5: 2371-2386.
  • Chen Q, Wang J, Yang S, Qin Y., Deng B., and Wei X, 2017. A real-time FPGA implementation of a biologically inspired central pattern generator network, Neurocomputing, 244, 63–80.
  • Elabbasy E M, Elsadany A A, and Zhang Y, 2014. Bifurcation analysis and chaos in a discrete reduced lorenz system. Applied Mathematics and Computation 228(2014), 184–194.
  • Ghaziani R K, Goverts K, Sonck C, 2012. Resonance and bifurcation a discrete time predator-prey system with Holling functional response. Nonlinear Analysis Real World Applications 13 (2012), 1451–1465.
  • Gleria IM, Figueiredo A, Rocha Filho, T M, 2001. Stability Properties of a General Class of Nonlinear Dynamical Systems. J.Phys A: Math. Gen. 34 3561-3575.
  • Goel NS, Maitra SC, and Montroll EW, 1971. On the Voltera and other nonlinear models of interacting populations. Rev. Modern Phys. 43, 231-276.
  • Gomar S, and Ahmadi A, 2014. Digital Multiplierless Implementation of Biological Adaptive-Exponential Neuron Model, IEEE Trans. Circuits Syst. I Regul. Pap., 61(4), 1206–1219.
  • He X, Liao M. & Xu C, 2011. Stability and Hopf Bifurcation analysis for a Lotka- Volterra predator-prey models with two delays, Int. J. Appl. Math. Comput., 21(1), 97- 107.
  • Kermack W O, and Mckendrick A G, 1927. A contribution to the mathematical theory of epidemics, Proceeding of Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700-72.
  • Kerner E H, 1957. The bulletin of mathematical biophysics. 19 (1957), 121.
  • Kimura M and Weiss G H, 1964. The stepping stone model of population structure and the decrease of genetic correlation with distance, Genetics 49 (1964), 561-576.
  • Korkmaz Tan R, and Bora Ş, 2019. Adaptive parameter tuning for agent-based modeling and simulation. Simulation: Transactions of the Society for Modeling and Simulation International, 95(9) 771-796.
  • Lotka A J, 1926. Elements of physical biology. Science Progress in the Twentieth Century, 21(82): 341-343.
  • Scheiner ER, 1996. Invitation to Dynamical Systems, The John Hopkins University Press, Washington, D.C.
  • Volterra V, 1978. Variazioni et fluttuazioni del numero d’individui in specie animali conviventi, Scudo ve Ziegler (Trans.), R. Comitato Talassografico Memoria, 6 (2), 31-113p.
  • Yener SC, Barbaros C, Mutlu R and Karakulak E, 2017. Implementation of Microcontroller-Based Memristive Chaotic Circuit, Acta Phys. Pol. A, 132(3), 1058–1061.
  • Yener ŞÇ, Barbaros C, Mutlu R and Karakulak E, 2018. Design of a Microcontroller-Based Chaotic Circuit of Lorenz Equations, in International Conference on Science and Technology ICONST 2018 5-9 September 2018 Prizren - KOSOVO, pp. 612–615.
  • Yener ŞÇ, Mutlu R, 2018. A Microcontroller-Based ECG Signal Generator Design Utilizing Microcontroller PWM Output and Experimental ECG Data, The Scientific Meeting on Electrical-Electronics Biomedical Engineering and Computer Science in 2018 (EBBT’2018) (18.04.2018-19.04.2018).
  • Yener SC, Mutlu R, 2019. - A Microcontroller Implementation Of Hindmarsh- Rose Neuron Model-Based Biological Central Pattern Generator, 1st International Informatics and Software Engineering Conference (UBMYK), 6-7 November 2019, Ankara.
  • Zhang G, Yi S and Boshan C, 2014. Bifurcation analysis in a discrete differential-algebraic predator-prey system. International Journal of Bifucation and Chaos, 38 (2014), 4559–4048.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Elektrik Elektronik Mühendisliği / Electrical Electronic Engineering
Yazarlar

Ertuğrul Karakulak 0000-0001-5937-2114

Rabia Korkmaz Tan 0000-0002-3777-2536

Reşat Mutlu 0000-0003-0030-7136

Yayımlanma Tarihi 1 Eylül 2021
Gönderilme Tarihi 3 Ekim 2020
Kabul Tarihi 10 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 11 Sayı: 3

Kaynak Göster

APA Karakulak, E., Korkmaz Tan, R., & Mutlu, R. (2021). STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations. Journal of the Institute of Science and Technology, 11(3), 1887-1895. https://doi.org/10.21597/jist.804591
AMA Karakulak E, Korkmaz Tan R, Mutlu R. STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations. Iğdır Üniv. Fen Bil Enst. Der. Eylül 2021;11(3):1887-1895. doi:10.21597/jist.804591
Chicago Karakulak, Ertuğrul, Rabia Korkmaz Tan, ve Reşat Mutlu. “STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations”. Journal of the Institute of Science and Technology 11, sy. 3 (Eylül 2021): 1887-95. https://doi.org/10.21597/jist.804591.
EndNote Karakulak E, Korkmaz Tan R, Mutlu R (01 Eylül 2021) STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations. Journal of the Institute of Science and Technology 11 3 1887–1895.
IEEE E. Karakulak, R. Korkmaz Tan, ve R. Mutlu, “STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations”, Iğdır Üniv. Fen Bil Enst. Der., c. 11, sy. 3, ss. 1887–1895, 2021, doi: 10.21597/jist.804591.
ISNAD Karakulak, Ertuğrul vd. “STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations”. Journal of the Institute of Science and Technology 11/3 (Eylül 2021), 1887-1895. https://doi.org/10.21597/jist.804591.
JAMA Karakulak E, Korkmaz Tan R, Mutlu R. STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations. Iğdır Üniv. Fen Bil Enst. Der. 2021;11:1887–1895.
MLA Karakulak, Ertuğrul vd. “STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations”. Journal of the Institute of Science and Technology, c. 11, sy. 3, 2021, ss. 1887-95, doi:10.21597/jist.804591.
Vancouver Karakulak E, Korkmaz Tan R, Mutlu R. STM32F429 Discovery Board-Based Emulator for Lotka-Volterra Equations. Iğdır Üniv. Fen Bil Enst. Der. 2021;11(3):1887-95.

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