Increasing average period lengths by switching of robust chaos maps in finite precision

Nagaraj, Nithin; Shastry, Mahesh C.; Vaidya, P. G.

doi:10.1140/epjst/e2008-00850-4

Cited by 53 publications

(33 citation statements)

References 16 publications

(22 reference statements)

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“…During last few years deterministic chaos systems (DCHS) are used instead of PRNGs. As was demonstrated in Pluhacek et al (2012aPluhacek et al ( , b, 2013, Persohn and Povinelli (2012), Chia and Tan (1991), Longa et al (1996), Dellago and Hoover (2000), Binder and Okamoto (2003) and Nagaraj et al (2008), very often is performance of EAs using DCHS better or fully comparable with EAs using PRNGs. See for example Pluhacek et al (2013).…”

Section: Introductionmentioning

confidence: 85%

“…Currently, there are research reports of theoretical and experimental analyses of the precision-dependent behavior of chaotic systems. Let us mention, for example, Persohn and Povinelli (2012), Chia and Tan (1991), Longa et al (1996), Dellago and Hoover (2000), Binder and Okamoto (2003) or Nagaraj et al (2008). Our approach here is in fact to repeat and expand of those results and its use instead of PRGNs inside evolutionary algorithms.…”

Section: Introductionmentioning

confidence: 97%

“…Till now chaos was observed in various systems (including evolutionary one) and in the last few years is also used to replace pseudo-random number generators (PRGNs) in evolutionary algorithms (EAs). Let us mention, for example, research papers like Zelinka et al (2010) (a comprehensive overview of mutual intersection between EAs and chaos is discussed here), one of the first use of chaos inside EAs (Caponetto et al 2003;Pluhacek et al 2012aPluhacek et al , b, 2013Persohn and Povinelli 2012;Chia and Tan 1991;Longa et al 1996;Dellago and Hoover 2000;Binder and Okamoto 2003;Nagaraj et al 2008) discussing use of deterministic chaos inside particle swarm algorithm instead of PRGNs, Lozi (2012), Wang and Qin (2012), Pareek et al (2010) and Wang and Yang (2012) investigating relations between chaos and randomness or the latest one Sun et al (2010), Wei-Chiang et al (2012), Senkerik et al (2012) and Davendra et al (2010) using chaos with EAs in applications, amongst the others.…”

Section: Introductionmentioning

confidence: 99%

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Investigation on evolutionary algorithms powered by nonrandom processes

et al. 2015

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Inherent part of evolutionary algorithms that are based on Darwin's theory of evolution and Mendel's theory of genetic heritage, are random processes since genetic algorithms and evolutionary strategies are used. In this paper, we present extended experiments (of our previous) of selected evolutionary algorithms and test functions showing whether random processes really are needed in evolutionary algorithms. In our experiments we used differential evolution and SOMA algorithms with functions 2ndDeJong, Ackley, Griewangk, Rastrigin, SineWave and StretchedSineWave. We use n periodical deterministic processes (based on deterCommunicated by R. Matousek. ministic chaos principles) instead of pseudo-random number generators (PRGNs) and compare performance of evolutionary algorithms powered by those processes and by PRGNs. Results presented here are numerical demonstrations rather than mathematical proofs. We propose the hypothesis that a certain class of deterministic processes can be used instead of PRGNs without lowering the performance of evolutionary algorithms.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Investigation on evolutionary algorithms powered by nonrandom processes

et al. 2015

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“…More unseen phenomena hidden in the continuous and discrete chaos deserve further exploration. There are many research reports of theoretical and experimental analysis for the precision-dependent behavior of chaotic systems [3][4][5][6][7]. The theory and approach are used to study the problem, which include the unstable periodic orbit in the attractor, the shadowing lemma, the number theory, the statistical analysis of probability theory and the combination of these.…”

Section: Introductionmentioning

confidence: 99%

The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map

Liu

Zhang

Song

2014

Entropy

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In this paper, we introduce an iterative method with lower positions of true numerical solutions located in the real orbit in order to investigate the property of the logistic map. The basic structure of the logistic map is presented, which consists of the root gene position, the common gene position and the individual gene position. The ergodicity and randomness of the logistic map are dependent on the individual gene position. We find that the lower positions of the true numerical solutions in the real orbits have the property of a half-life.

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“…They show that the period map can be generated by a single, autonomous vector field, generalizing a result which was previously known only for linear systems. Nagaraj et al [7] study how the period of numerically simulated chaotic maps, which are finite because of the limited accuracy of floating-point calculations, is affected by on-off switching of chaotic motion. They find that the average period increases for random switching of chaos, and use this to implement a chaotic random number generator.…”

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confidence: 99%

Chaos and nonlinear dynamics: Advances and perspectives

Károlyi

Moura

Romano

et al. 2008

Eur. Phys. J. Spec. Top.

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Chaotic behaviour of nonlinear systems has been one of the most fruitful additions to physics and applied mathematics in the latter part of the twentieth century. It has evolved into a mature discipline, which keeps researchers active in many areas of science. This special issue of the European Physical Journal is dedicated to reporting the latest advances in that area. The papers collected here span the full spectrum of the field, and show that it continues to be an exciting and active area of research. We have grouped all papers into four sections: a theoretical section, a section about synchronisation, a section on fluid dynamics, and a section on applications. We will now briefly address each paper and outline the most important results.Despite the fact that Dynamical Systems is a mature area of science, its fundaments and theoretical basis are still a source of many fascinating problems. One of the most exciting areas of dynamical systems theory is high-dimensional Hamiltonian dynamics. An important problem in the numerical study of Hamiltonian systems of high dimension is to efficiently compute the slow diffusion of trajectories near quasiperiodic tori. The first paper in this collection addresses this issue, and proposes an efficient method to calculate the GALI k coefficients, based on the singular value decomposition algorithm; the authors use their method to understand diffusion and other issues in the Fermi-Pasta-Ulam system [1].Another crucial area within the theory of dynamical systems deals with the development of time-series analysis techniques. Since Takens' theorem, embedding and time-series analysis have been the corner stones of many applications of dynamical systems theory. These topics also have a rich theoretical background, which is a research topic of its own. Vaidya and Majumder [2] investigate the cause of spurious instabilities often found in model equations reconstructed from time series data; they find that this is related to a topological foliation caused by the embedding. Henschel et al.[3] develop a multi-variate analysis method to adapt time-series analysis techniques for point processes -that is, data consisting of only a set of time points where a certain event happened, such as the firing of a neuron; this is crucial for the analysis of biomedical data. Kwasniok [4] tackles yet another aspect of time-series analysis: predictability. By fitting a hidden Markov chain model to time series data, he is able to predict the probabilities of visiting specific regions in phase space; the method is validated with the forced Lorenz system.Another major area in the theory of dynamical systems is bifurcation analysis. Non-smooth dynamical systems are well known for the rich set of bifurcations they display. Taralova [5] investigates a new bifurcation found in a particular class of piece-wise linear maps; this bifurcation leads to the creation of a chaotic orbit. A different kind of non-smoothness is studied by Pokorny and Klic in their paper [6], wherein they investigate the dynamics of a ...

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Increasing average period lengths by switching of robust chaos maps in finite precision

Cited by 53 publications

References 16 publications

Investigation on evolutionary algorithms powered by nonrandom processes

Investigation on evolutionary algorithms powered by nonrandom processes

The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map

Chaos and nonlinear dynamics: Advances and perspectives

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