Period Three Begins

  title={Period Three Begins},
  author={Cheng Zhang},
  journal={Mathematics Magazine},
  pages={295 - 297}
  • C. Zhang
  • Published 1 October 2010
  • Mathematics
  • Mathematics Magazine
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. 
Cycles of the Logistic Map
  • Cheng Zhang
  • Mathematics, Computer Science
    Int. 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
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.
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
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
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
  • P. Harsha
  • Computer Science
    IEEE 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.
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
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
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.
Indoor optical wireless communications supporting secure multiple access


Simple mathematical models with very complicated dynamics
  • R. May
  • Computer Science, Medicine
  • 1976
This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Nonlinear Dynamics And Chaos
The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.
The Birth of Period Three
Xn+l = rXnO -Xn),(1) where 0 < x_ 1 and 0 < r < 4. In other words, given some starting number 0 < xl < 1, we generate a new number x2 by the rule x2 = rx1(1 x 1), and then repeat the process to
Period-3 Orbits via Sylvester's Theorem and Resultants
1. D. K. Biss, On the Symmetry Groups of Hypergraphs of Perfect Cwatsets, Ars Combinatoria, to appear. 2. C. M. Girod, M. Lepinski, J. R. Mileti and J. R. Paulhus, Cwatset Isomorphism and its
Period Three Trajectories of the Logistic Map
The Birth of Period 3, Revisited
Nonlinear Dynamics and Chaos, Addison-Wesley
  • 1994