Input-Output Mechanism of the Discrete Chaos Extension

AKHMET M., Fen M. O.

5th International Conference on Nonlinear Science and Complexity (NSC), Xian, China, 4 - 09 August 2014, vol.15, pp.203-233 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 15
  • Doi Number: 10.1007/978-3-319-28764-5_7
  • City: Xian
  • Country: China
  • Page Numbers: pp.203-233
  • TED University Affiliated: No

Abstract

In this chapter the extension of chaos in difference equations is discussed. The theoretical results are based on chaos in the sense of Devaney and period-doubling cascades. The existence of homoclinic and heteroclinic orbits is rigorously proved, and a theoretical control technique for the extended chaos is proposed. The results are supported with the aid of simulations. Arbitrarily high-dimensional chaotic discrete-time dynamical systems can be designed by means of the presented technique. A discrete gonorrhea model is utilized to generate chaotic behavior in population dynamics.