<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.</p>
</abstract>

In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map"}

In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback...

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

Published Online: Nov 23, 2021

Page range: 201 - 227

Received: Jan 08, 2021

Accepted: Feb 19, 2021

DOI: https://doi.org/10.2478/auom-2021-0041

Keywords
Standard logistic sine square map, periodic and fixed points, chaos, time series plot, bifurcation plot, Lyapunov exponent (LE)

© 2021 Sudesh Kumari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map

Published Online: Nov 23, 2021

Page range: 201 - 227

Received: Jan 08, 2021

Accepted: Feb 19, 2021

DOI: https://doi.org/10.2478/auom-2021-0041

KeywordsStandard logistic sine square map, periodic and fixed points, chaos, time series plot, bifurcation plot, Lyapunov exponent (LE)

© 2021 Sudesh Kumari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Standard logistic sine square map, periodic and fixed points, chaos, time series plot, bifurcation plot, Lyapunov exponent (LE)