# Period Three Begins

@article{Zhang2010PeriodTB, title={Period Three Begins}, author={Cheng Zhang}, journal={Mathematics Magazine}, year={2010}, volume={83}, pages={295 - 297} }

Summary By exploiting the geometry of the cobweb plot, we provide a simple and elementary derivation of the parameter for the period-three cycle of the logistic map.

## 10 Citations

Cycles of the Logistic Map

- Mathematics, Computer ScienceInt. J. Bifurc. Chaos
- 2014

The onset and bifurcation points of n-cycles of several polynomial maps are located through a characteristic equation connecting cyclic polynomials of the cycle points. The polynomials satisfied by…

Complexity modeling and analysis of chaos and other fluctuating phenomena

- Mathematics, PhysicsChaos, Solitons & Fractals
- 2018

Abstract The refined composite multiscale-entropy algorithm was applied to the time-dependent behavior of the Weierstrass functions, colored noise, and Logistic map to provide the fresh insight into…

Visibility graphlet approach to chaotic time series.

- Computer Science, MedicineChaos
- 2016

The results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.

High-sensitivity image encryption algorithm with random cross diffusion based on dynamically random coupled map lattice model

- Computer Science
- 2021

By analyzing simulation performance of encryption, it can be easily determined that the algorithm has a high degree of security, highly sensitive, good statistical performance and it further demonstrates the excellent features of the PDRCML model.

Hybrid Chaotic Chemical Reaction Optimization for Multiple- Choice Knapsack Problem

- 2020

This paper proposes an algorithm based on metaheuristic chemical reaction optimization and chaotic map for multiple-choice knapsack problem (MCKP). MCKP is a well-known NP-hard problem and it has a…

A Novel Micro-Architecture Using a Simplified Logistic Map for Embedded Security

- Computer ScienceIEEE Embedded Systems Letters
- 2017

This letter develops a micro-architecture that involves the proposed chaos generator and discusses the control methods by which data is to be handled for seamless encryption/decryption without processor involvement.

Secure multiple access for indoor optical wireless communications with time-slot coding and chaotic phase.

- Computer Science, MedicineOptics express
- 2017

A novel mechanism to simultaneously provide secure connections for multiple users in indoor optical wireless communication systems by employing the time-slot coding scheme together with chaotic phase sequence is reported.

PUF-Based Secure Chaotic Random Number Generator Design Methodology

- Computer ScienceIEEE Transactions on Very Large Scale Integration (VLSI) Systems
- 2020

This work proposes a novel physical unclonable function-based CPRNG (PUF-CPRNG), where the initial seed is secured by generating it from PUF, and includes dynamic refreshing logic to ensure that the random numbers generated are nonperiodic.

Permutation Entropy for Graph Signals

- Computer Science, MathematicsArXiv
- 2021

This work defines for the first time an entropy metric to analyse signals measured over irregular graphs by generalising permutation entropy, a well-established nonlinear metric based on the comparison of neighbouring values within patterns in a time series.

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