[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Dynamical Analysis and Multisim Simulation of a New 4D Generalized Hamiltonian System

Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 427--438 | DOI:10.5890/DNC.2025.06.014

Karam N. Abdul-Kareem, Saad Fawzi Al-Azzawi

Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq

Download Full Text PDF

 

Abstract

This paper constructed a new 4D hyperchaotic system based on the generalized Hamiltonian forms. Through analysis of fundamental dynamical properties, including equilibrium points, stability, dissipative and conservative behaviors, bifurcation diagram, and Lyapunov exponents both numerically and analytically, this system exhibits a rich of dynamic features, encompassing hyperchaotic, chaotic, chaotic 2-tours, and periodic behaviors under certain parameters. Furthermore, the system is translated into an analog electronic circuit and simulated using an oscilloscope device, which achieved consistency between the MATLAB 2021 and Multisim 14.2 software simulations.

References

  1. [1]  Dodd, P.J. (2004), Disentanglement by dissipative open system dynamics, Physical Review A, 69(5), 052106.
  2. [2]  Marani, M., Banavar, J.R., Caldarelli, G., Maritan, A., and Rinaldo, A. (1998), Stationary self-organized fractal structures in an open, dissipative electrical system, Journal of Physics A: Mathematical and General, 31(18), L337.
  3. [3]  Kortus, J., Hellberg, C.S., and Pederson, M.R. (2001), Hamiltonian of the V 15 spin system from first-principles density-functional calculations, Physical Review Letters, 86(15), 3400.
  4. [4]  Navrotskaya, I., Soudackov, A.V., and Hammes-Schiffer, S. (2008), Model system-bath Hamiltonian and nonadiabatic rate con-stants for proton-coupled electron transfer at electrode-solution interfaces, The Journal of Chemical Physics, 128(24),
  5. [5]  Wang, Y., Ueda, K., and Bortoff, S.A. (2013), A Hamiltonian approach to compute an energy efficient trajectory for a servomotor system, Automatica, 49(12), 3550-3561.
  6. [6]  Mulero-Mart{i}nez, J.I. (2008), Canonical transformations used to derive robot control laws from a port-controlled Hamiltonian system perspective, Automatica, 44(9), 2435-2440.
  7. [7]  Sun, Y.Z., Cao, M., Shen, T.L., and Song, Y.H. (2002), Passivation controller design for turbo-generators based on generalised Hamiltonian system theory, IEE Proceedings-Generation, Transmission and Distribution, 149(3), 305-309.
  8. [8]  Cang, S.J., Chen, Z.Q., and Yuan, Z.Z. (2008), analysis of an on-off intermittency system with adjustable state levels, Kybernetika, 44(4), 455-468.
  9. [9]  Cang, S., Qi, G., and Chen, Z. (2010), A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system, Nonlinear Dynamics, 59, 515-527.
  10. [10]  Cang, S., Wu, A., Wang, Z., Xue, W., and Chen, Z. (2016), Birth of one-to-four-wing chaotic attractors in a class of simplest three-dimensional continuous memristive systems, Nonlinear Dynamics, 83, 1987-2001.
  11. [11]  Cang, S., Wu, A., Wang, Z., Wang, Z., and Chen, Z. (2016), A general method for exploring three-dimensional chaotic attractors with complicated topological structure based on the two-dimensional local vector field around equilibriums, Nonlinear Dynamics, 83, 1069-1078.
  12. [12]  Lorenz, E.N. (1963), Deterministic nonperiodic flow, Journal of atmospheric sciences, 20(2), 130-141.
  13. [13]  R\"{o}ssler, O.E. (1976), An equation for continuous chaos, Physics Letters A, 57(5), 397-398.
  14. [14]  Chen, G. and Ueta, T. (1999), Yet another chaotic attractor, International Journal of Bifurcation and Chaos, 9(07), 1465-1466.
  15. [15]  L\"{u}, J. and Chen, G. (2002), A new chaotic attractor coined, International Journal of Bifurcation and chaos, 12(03), 659-661.
  16. [16]  Liu, C., Liu, T., Liu, L., and Liu, K. (2004), A new chaotic attractor, Chaos, Solitons and Fractals, 22(5), 1031-1038.
  17. [17]  Sprott, J.C. (1994), Some simple chaotic flows, Physical Review E, 50(2), R647.
  18. [18]  Sprott, J.C. (2011), A proposed standard for the publication of new chaotic systems, International Journal of Bifurcation and Chaos, 21(09), 2391-2394.
  19. [19]  Cang, S., Wu, A., Wang, Z., and Chen, Z. (2017), On a 3-D generalized Hamiltonian model with conservative and dissipative chaotic flows, Chaos, Solitons and Fractals, 99, 45-51.
  20. [20]  Aguilar‐Iba\~{n}ez, C., Mendoza‐Mendoza, J.A., Martinez, J.C., de Jesus Rubio, J., and Suarez‐Castanon, M.S. (2015), A limit set stabilization by means of the Port Hamiltonian system approach, International Journal of Robust and Nonlinear Control, 25(12), 1739-1750.
  21. [21]  Li, C. and Wang, Y. (2013), Input disturbance suppression for port-controlled hamiltonian system via the internal model method, International Journal of Control, Automation and Systems, 11, 268-276.
  22. [22]  Fadhel, S.A., Al-Kateeb, Z.N., and AL-Shamdeen, M.J. (2021), An improved data hiding using pixel value difference method and hyperchaotic system, In Journal of Physics: Conference Series, 1879(2), 022089.
  23. [23]  Al-Kateeb, Z.N. and Jader, M. (2024), Multi level of encryption and steganography depending on Rabinovich Hyperchaotic System and DNA, Multimedia Tools and Applications, 1-27.
  24. [24]  Mohammed, N.M. and Al-Kateeb, Z.N. (2022), A new secure encryption algorithm based on RC4 cipher and 4D hyperchaotic Sprott-S system, In 2022 Fifth College of Science International Conference of Recent Trends in Information Technology (CSCTIT), 131-136.
  25. [25]  AL-Azzawi, S.F., Rubiani, H., Sukono, A.S., and Nainggolan, N. (2020), Chaotic Lorenz system and it's suppressed, Journal of Advanced Research in Dynamical and Control Systems, 12(2), 548-555.
  26. [26]  Aziz, M.M. and Al-Azzawi, S.F. (2021), A modification of nonlinear feedback controller, International Journal of Computing Science and Mathematics, 13(1), 64-79.
  27. [27]  Al-Obeidi, A.S. and Al-Azzawi, S.F. (2022), A novel six-dimensional hyperchaotic system with self-excited attractors and its chaos synchronisation, International Journal of Computing Science and Mathematics, 15(1), 72-84.
  28. [28]  AL-Azzawi, S.F. and Al-Obeidi, A.S. (2021), Chaos synchronization in a new 6D hyperchaotic system with self-excited attrac-tors and seventeen terms, Asian-European Journal of Mathematics, 14(05), 2150085.
  29. [29]  Khattar, D., Agrawal, N., and Sirohi, M. (2024), Qualitative analysis of a new 6D hyper-chaotic system via bifurcation, the Poincar{e} notion, and its circuit implementation, Indian Journal of Physics, 98(1), 259-273.
  30. [30]  Al-Talib, Z.S. and Al-Azzawi, S.F. (2023), New simple 6D hyperchaotic system with hyperbolic equilibrium and its electronic circuit, Iraqi Journal for Computer Science and Mathematics, 4(1), 155-166.
  31. [31]  Al-Azzawi, S.F. (2012), stability and bifurcation of pan chaotic system by using Routh--Hurwitz and Gardan methods, Applied Mathematics and Computation, 219(3), 1144-1152.
  32. [32]  Khan, N. and Muthukumar, P. (2022), Transient chaos, synchronization and digital image enhancement technique based on a novel 5D fractional-order hyperchaotic memristive system, Circuits, Systems, and Signal Processing, 41(4), 2266-2289.
  33. [33]  Khattar, D., Agrawal, N., and Sirohi, M. (2023), Dynamical analysis of a 5D novel system based on Lorenz system and its hybrid function projective synchronisation using adaptive control, Pramana, 97(2), 76.
  34. [34]  Wolf, A., Swift, J.B., Swinney, H.L., and Vastano, J.A. (1985), Determining Lyapunov exponents from a time series, Physica D: Nonlinear Phenomena, 16(3), 285-317.
  35. [35]  Singh, J.P. and Roy, B.K. (2016), The nature of Lyapunov exponents is $(+,+,-,-)$. Is it a hyperchaotic system? Chaos, Solitons and Fractals, 92, 73-85.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates