Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 29, Issue 12, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127419501682
Keywords
Nonautonomous system; stable node-focus; hidden oscillation; multiplierless circuit
Funding
- National Natural Science Foundations of China [51777016, 61801054, 51607013, 61601062]
- Natural Science Foundations of Jiangsu Province, China [BK20160282]
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This paper presents a simple two-dimensional nonautonomous system, which possesses piecewise linearity constructed by a simple absolute value function. The nonautonomous system has only one switchable equilibrium state with a stable node-focus in the considered control parameter region but can generate periodic, chaotic and coexisting attractors. Therefore, the presented simple two-dimensional nonautonomous system always operates with hidden oscillations, which is not similar to any example reported in the literature. Furthermore, specific hidden dynamical behaviors are numerically disclosed by employing one-dimensional and two-dimensional bifurcation plots, phase plane plots, Poincare mappings, local attraction basins, and complexity plots. In addition, by utilizing the circuit module of the absolute value function, a multiplierless analog circuit is designed, based on which breadboard experiments are performed to validate the numerically simulated phase plane plots of coexisting attractors.
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