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Mathematical Methods in Modern Complexity Science

Part of the Nonlinear Systems and Complexity Book Series (volume 33)

Editors: Volchenkov, Dimitri; Tenreiro Machado, J. A.

DOI: 10.1007/978-3-030-79412-5

ISBN: 978-3-030-79411-8

Publisher: Springer International Publishing - Springer Journals

Jul 1, 2021

1 - 10 of 11 Chapters

LitStream

Chapter 1Shannon Information Analysis of the Chromosome Code

Tenreiro Machado, J. A.

Pages: 1 –12

[This chapter studies the chromosome information content. Several statistics considering different number of bases for alphabet character encoding are derived. Based on the resulting histograms, word delimiters and character relative frequencies are identified. The knowledge of this data leads to...
LitStream

Chapter 2An Unfair Coin of the Standard & Poor’s 500

Volchenkov, Dimitri; Smirnov, Veniamin

Pages: 13 –31

[Based on the available data, we reconstructed a discrete model of S&P 500 stock market phase space and assessed predictability of market events as well as the amounts of predictable and unpredictable information in the historical data over the different time horizons. Inhomogeneous density of...
LitStream

Chapter 3Relativistic Chaotic Scattering

Bernal, Juan D.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

Pages: 33 –62

[The phenomenon of chaotic scattering is very relevant in different fields in science and engineering, and it has been mainly studied in the context of Newtonian mechanics. In this chapter, we study the chaotic scattering considering the special relativity, not just for high velocities but also...
LitStream

Chapter 4Complex Dynamics of Solitons in Rotating Fluids

Ostrovsky, Lev A.; Stepanyants, Yury A.

Pages: 63 –78

[Interaction of solitons with a long background wave is studied within the framework of rotation modified Korteweg–de Vries (rKdV) equation. Using the asymptotic method for solitons interacting as classical particles with a long wave, we derive a set of ODEs describing soliton amplitude and its...
LitStream

Chapter 5Multistability Coexistence of Memristive Chaotic System and the Application in Image Decryption

Min, Fuhong; Li, Chuang

Pages: 79 –97

[In this chapter, based on the active charge-controlled memristive Chua’s circuit, multiple coexisting attractors depending on the memristor initial values and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. With the system motion...
LitStream

Chapter 6Extreme Events and Emergency Scales

Smirnov, Veniamin; Ma, Zhuanzhuan; Volchenkov, Dimitri

Pages: 99 –128

[An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon’s entropy calculated on the probability that the...
LitStream

Chapter 7Probability Entanglement and Destructive Interference in Biased Coin Tossing

Volchenkov, Dimitri

Pages: 129 –140

[Some uncertainty about flipping a biased coin can be resolved from a sequence of the coin sides already shown. The side repeating probabilities assumed to be independent in integer time get entangled with one another in fractional time, and the degree of entanglement changes over (fractional)...
LitStream

Chapter 8On the Solvability of Some Systems of Integro-Differential Equations with Drift

Efendiev, Messoud; Vougalter, Vitali

Pages: 141 –167

[We establish the existence in the sense of sequences of solutions for certain systems of integro-differential equations involving the drift terms in the appropriate H2 spaces by means of the fixed point technique when the elliptic problems contain second order differential operators with and...
LitStream

Chapter 9Solvability in the Sense of Sequences for Some non Fredholm Operators with the Bi-Laplacian

Vougalter, Vitali; Volpert, Vitaly

Pages: 169 –181

[We study solvability of some linear nonhomogeneous elliptic problems and prove that under reasonable technical conditions the convergence in L2(ℝd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
LitStream

Chapter 10The Preservation of Nonnegativity of Solutions of a Parabolic System with the Bi-Laplacian

Vougalter, Vitali

Pages: 183 –188

[The paper deals with the easily verifiable necessary condition of the preservation of the nonnegativity of the solutions of a system of parabolic equations involving the bi-Laplace operator. This necessary condition is vitally important for the applied analysis community because it imposes the...

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