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Switching induced complex dynamics in an extended logistic map

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  • Levinsohn, Erik A.
  • Mendoza, Steve A.
  • Peacock-López, Enrique

Abstract

Switching strategies have been related to the so-called Parrondian games, where the alternation of two losing games yields a winning game. We can consider two dynamics that, by themselves, yield different simple dynamical behaviors, but when alternated, yield complex trajectories. In the analysis of the alternate-extended logistic map, we observe a plethora of complex dynamic behaviors, which coexist with a super stable extinction solution.

Suggested Citation

  • Levinsohn, Erik A. & Mendoza, Steve A. & Peacock-López, Enrique, 2012. "Switching induced complex dynamics in an extended logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 426-432.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:4:p:426-432
    DOI: 10.1016/j.chaos.2011.12.020
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    References listed on IDEAS

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    1. Doering, Charles R., 1998. "Stochastic ratchets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 1-6.
    2. Amengual, P. & Meurs, P. & Cleuren, B. & Toral, R., 2006. "Reversals of chance in paradoxical games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 641-648.
    3. Buceta, J. & Lindenberg, Katja, 2003. "Patterns in reaction–diffusion systems generated by global alternation of dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 230-242.
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    Cited by:

    1. Mendoza, Steve A. & Matt, Eliza W. & Guimarães-Blandón, Diego R. & Peacock-López, Enrique, 2018. "Parrondo’s paradox or chaos control in discrete two-dimensional dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 86-93.
    2. Kumar, Deepak & Rani, Mamta, 2022. "Alternated superior chaotic variants of gravitational search algorithm for optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Yadav, Anju & Rani, Mamta, 2015. "Alternate superior Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 1-9.
    4. Mendoza, Steve A. & Peacock-López, Enrique, 2018. "Switching induced oscillations in discrete one-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 35-44.
    5. Silva, Emily & Peacock-Lopez, Enrique, 2017. "Seasonality and the logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 152-156.

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