abstract

• In this paper, we investigate the dynamical behavior of a one-dimensional piecewise map based on the logistic map, where generalized multistability can be observed. The proposed system has the unique property that the function is symmetric with respect to the origin but not its behavior, furthermore this system can display three types of multistability, and chaos for both, monostable and bistable behaviors. The stability analysis of the proposed system is presented. We describe the structure of bistable regions in the bifurcation diagram. Particular attention is paid to the chaotic regions. Corresponding to coexisting attractors, three scenarios of coexisting attractors, namely fixed points, periodic orbits, and chaotic attractors, can be found, which are unreported behaviors in discrete chaotic systems. The mechanism that leads to multistability phenomenon including pitchfork bifurcation, period-halving bifurcations, and the coexisting invariant sets is demonstrated. Furthermore, the Lyapunov exponent is analyzed with the type of multistability distinguished for a given set of parameters. © World Scientific Publishing Company.

authors

• Gilardi-Velázquez H.E.

publication date

• 2022-01-01

funding provided via

• Consejo Nacional de Ciencia y Tecnología, CONACYT: 2495713, A1-S-30433  Grant

published in

• International Journal of Bifurcation and Chaos  Journal

keywords

• bifurcation analysis; chaos; logistic map; Multistability; piecewise system Chaotic systems; Lyapunov methods; Bifurcation analysis; Bistables; Co-existing attractors; Dynamical behaviors; Logistic maps; Multistability; One-dimensional piecewise maps; Piece-wise; Piecewise systems; Property; Bifurcation (mathematics)

Digital Object Identifier (DOI)

• 10.1142/S0218127422502418

PubMed ID

start page

end page

volume

• 32

issue

• 16