The Paradigm of Complex Probability, Numerical Analysis, and Chaos Theory | Book Publisher International

The set of imaginary numbers is taken into account by extending the probability system of five axioms of Andrey Nikolaevich Kolmogorov which was put forward in 1933. This is achieved by adding three new and supplementary axioms. Hence, any random experiment can thus be performed in the extended complex probability set C = R + M which is the sum of the real set R of real probabilities and the imaginary set M of imaginary probabilities. The objective here is to determine the complex probabilities by encompassing and considering additional new imaginary dimensions to the event that occurs in the “real” laboratory. The outcome of the stochastic phenomenon in C can be foretold perfectly whatever the probability distribution of the input random variable in R is since the corresponding probability in the whole set C is permanently and constantly equal to one. Thus, the consequence that follows indicates that randomness and chance in R is substituted now by absolute determinism in C. This is the result of the fact that the probability in C is computed after the subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic experiment. This novel complex probability paradigm will be applied to numerical analysis and to chaos theory to prove henceforth that chaos vanishes totally and completely in the probability universe C = R + M.

Author(s) Details:

Abdo Abou Jaoudé,
Department of Mathematics and Statistics, Faculty of Natural and Applied Sciences, Notre Dame University-Louaize, Lebanon.

Please see the link here: https://stm.bookpi.org/TPCPNACT/article/view/14275

A Way to Supress Chaos in the Cubic-Quintic Duffing Van der Pol Equation | Chapter 7 | Research and Applications Towards Mathematics and Computer Science Vol. 9

In this paper we apply several techniques to achieve analytic approximate and numerical solutions of the cubic–quintic Duffing–van der Pol equation. This equation represents a second-order ordinary differential equation with quintic nonlinearity and includes two external periodic forcing terms. We permorm Melnikov analysis in order to detect chaotic beahvior.

Author(s) Details:

Alvaro H. Salas S.,
Universidad Nacional de Colombia, Fizmako Research Group, Bogotá, Colombia.

Please see the link here: https://stm.bookpi.org/RATMCS-V9/article/view/13332

Complexity in Dynamic Academic Systems from Topology and Genetic Grammars | Chapter 13 | Research Highlights in Language, Literature and Education Vol. 6

 This affiliate sheds a new light on the hypothetical foundations of the main contemporary drives towards the adequacy of the education-learning process to the excellent changes of our society. An academic environment can progress from chaos to stabilised states, and this hypothetical study will present and also discuss a turbulent simulation model that addresses this. This study will determine a consistent institution for new methodological initiatives that support shifts in the usual paradigm of instruction and learning.The study was planned from the classical literature on disorganized systems accompanying some original hypothetical implementations.This study is based on the configuration of a DAS toy model by way of computational simulations carried out on a practically built haphazard academic environment. The individuals were top-secret by profiles of orderly abilities represented by twofold strings outlining a topology. Such the earth's features fixed the type of the strings and their transcriptions to unit of the mathematical system system. To imitate the evolution of bureaucracy, three differential equations were numerically linked in convolution, individual of which fashioned reference to those strings transfered into decimal signs. The simulations were run using the Maple and R programming languages.Simulations displayed attractors for different occasion intervals of redundancies. For wide ranges of individual propensities to cultivate the six abilities illustrated in the work it was noticed that the dissimilarities of individual profiles induced attractors accompanying narrow boundaries. Growing the number of things, this tendency was uphold.   The study displayed simulations of academic systems containing professors and researchers communicating in a stable environment, emphasize how these structures could change from chaotic configurations to stability and produce clear attractors.

Author(s) Details:

Nilo Serpa,
Centro Universitário ICESP, Brasília,Brazil.

Marcelo Alcântara,
Centro Universitário ICESP, Brasília,Brazil.

Emilly Moura da Cruz,
GAUGE-F Scientific Researches, Brazil.

Please see the link here: https://stm.bookpi.org/RHLLE-V6/article/view/10809

Chaotic Dynamics for Laser Diode under Unidirectional and Mutual Optical Injection with Optoelectronic Feedback| Chapter 9 | Current Overview on Science and Technology Research Vol. 8

 Nonlinear and anarchic dynamics for a continuous diffusion (CW) laser diode accompanying a Fabry-Perot cavity are being investigated tentatively to develop a new turbulent transmitter system. Uni-directional and bi-directional optical needle configurations were constructed accompanying and without optoelectronic feedback (OEFB) and even direct timbre. Another possibility is too investigated, where the needle is reversed to note dynamics generated in the second ray of light diode (LD2). Accordingly, the first laser diode (LD1) receives ocular injection from LD2, that is initially mixed with self-OEFB, and before, LD2, under OEFB, receives clean optical injection from LD1. Results signify the generation of turbulent pulsation with fashion hopping in the first arrangement and mode-lock at a specific bias current level in the second individual.Under bi-directional optical injection, results show that the ray of light entered a new inconstancy leading to a variety of more nonlinearities. One of bureaucracy is the lasing mode switching and switching. The ratio of OI was conditional an optical attenuator and again OEFB by an RF attenuator. Mode hopping, multimode emission, fad lock, and chaotic demeanor are all observed experimentally equivalent to operating conditions. The noticed chaotic pulse linewidth was calculated at 300 MHz, with the ability expected broader by way of changing detuning and injection percentage. The laser altered to emit in pulsation accompanying a route to chaos rank in which it has an FWHM of around 0.1GHz. Reversing dose led to linewidth augmentation with a very sharp FWHM, 1.5 kHz. Laser emission is troubled due to mixed dose as if it works accompanying OEFB, where the gain switches tend to drive the ray of light into pulsing states inferred by that positive OEFB. For each achieved result, skilled exists an use, such as; chaos shifts keying, commonness mixing, and up-adaptation to a new frequency to reduce the cost of speedy electronics guide optical communications.

Author(s) Details:

Ayser A. Hemed,
Department of Physics, College of Education, Mustansiriyah University, Baghdad, Iraq.

Rasha Salah Abbas,
First Karkh Directorate of Education, Ministry of Education, Baghdad, Iraq.

Please see the link here: https://stm.bookpi.org/COSTR-V8/article/view/8666

Application of Chaos Theory, Thermodynamics and AI in the Analysis of the Behavior of Complex Systems | Chapter 5 | New Frontiers in Physical Science Research Vol. 3

 This division is devoted to the hypothetical and practical facets of the application of chaos theory. The objects of research are involved nonlinear information arrangements. Methods for studying the performance of multidimensional nonlinear facts systems operating within the foundation of the Open System are presented. It concede possibility be noted that the physics of open structures develops a united approach to the description of a wide type of non-linear experiences. Using the achievements of aforementioned scientific fields as theory of randomness, thermodynamics, visual thinking and artificial intelligence, it is likely to discover secret patterns and additional information when studying aforementioned complex systems. In studies of the dynamics of complex methods, various characteristic signs are used. To study the incident processes of a dynamic arrangement in time, Poincare return times, Lyapunov exponents, Tsallis deterioration, fractal dimensions of bureaucracy, stability limits, etc. are used. In the ending part of the chapter, all these educational characteristic indicators of bureaucracy under study are projected to be secondhand for the input layer of the Recurrent Neural Network of the open ocean Learning Artificial Intelligence algorithm. The issues of imagination of measurement results and sciences concerned with information using the "Visual Thinking" science are considered. In the examples likely, due attention command a price of to the issues of modern imagination, which is the support for the implementation of the "Visual Thinking" science in research activities. The analysis of optical information distinguishing the dynamics of the limits of the system substitute will increase the speed of assessing its conduct, as well as the lawfulness of the decisions fashioned on its control.

Author(s) Details:

Bahram Ismailov,
Department of Instrument Engineering, Azerbaijan State Oil and Industry University, Azerbaijan.

Please see the link here: https://stm.bookpi.org/NFPSR-V3/article/view/8590

Studies on the Dynamics of Market Share’s Growth and Competition in Quadratic Mappings | Chapter 8 | Current Aspects in Business, Economics and Finance Vol.5

 This chapter demonstrates that the observed affair of any request, placed within the confine of a quadratic chart, can characterize the state of that request. Such a strategy explains the increase of request shares and their implicit troubles, the goods of broken scaling harmony, and the boundaries of company competition for request shares.

Author(s) Details:

C-René Dominique,
Laval University, Québec, Canada.

Luis Eduardo Rivera Solis,
Townsend School of Business, Dowling College, New York, USA.

Please see the link here: https://stm.bookpi.org/CABEF-V5/article/view/8455

Local Dynamics of a Discrete-time Host-Parasitoid Model | Chapter 9 | Novel Research Aspects in Mathematical and Computer Science Vol. 6

 

 We examine a non-dimensionalized Nicholson and Bailey discrete-time host-parasitoid model in this chapter. Phase portraits are created for several parameter ranges to display the system's intricate dynamics. We do the bifurcation analysis for the intrinsic growth rate r and the searching efficiency a. Numerous complicated dynamics, such as chaos and periodic windows, are visible. We provide a path to chaotic dynamics via period-doubling bifurcations. For b a, where a, b are searching efficiency, conditions of occurrence of the period-doubling, Neimark-Sacker, and saddle-node bifurcations are investigated. We look at stable and unstable manifolds for different equilibrium points and the presence of different attractors at this non-dimensionalized system. In the absence of the Ricker model, the host population exhibits behaviours that are consistent with parasitoid With the intraspecific information gained from the current work, we were better able to understand the dynamical behaviour of host-parasitoid interactions, which may be used to improve the conventional biological management of parasitoids.

Author(s) Details:

Tahmineh Azizi,
Department of Mechanical Engineering, Florida State University, Tallahassee, FL, USA.

Please see the link here: https://stm.bookpi.org/NRAMCS-V6/article/view/7768  

Harmonic Solutions Analysis and Floquet Theory in a Nonlinear Dissipative Hybrid Oscillator | Chapter 8 | Novel Research Aspects in Mathematical and Computer Science Vol. 5

The major goal is to investigate how the traditional Rayleigh-Duffing oscillator is modified by the novel nonlinear cubic, pure quadratic, and hybrid dissipative components. Similar to this, depending on their field of application, the parameters included are utilised to impose a regular, quasi-periodic, or even chaotic behaviour on the systems depicted by this oscillator. We study hysteresis, quasiperiodicity, and chaoticity in a nonlinear dissipative hybrid oscillator. A modified Rayleigh-Duffing oscillator will be used. The traditional Rayleigh-Duffing oscillator is modified by the novel nonlinear cubic, pure quadratic, and hybrid dissipative components at the same time. A detailed investigation of how each of these novel parameters affects the oscillator's dynamics has produced some surprising findings. It is obvious that any of these novel dissipation factors may be employed to modify the oscillator's dynamics. Hysteresis, amplitude jump, and resonance phenomena may be exploited to minimise or eliminate them in some cases, while they may be amplified in others. These new parameters can also be used to force a regular, quasi-periodic, or even chaotic behaviour on the systems represented by this oscillator, depending on their area of use. One of the early findings is the equation of the curve defining the zone of instability of the harmonic oscillation amplitudes. In order to regulate and anticipate the loss or gain of energy during this jump, it is therefore feasible to know the zone of amplitude authorised or the amplitude leap for the systems using this equation. The second stability of the system's oscillations is investigated, along with the impact of the dissipation parameters on this stability, it is concluded. It is important to keep in mind that the effect of certain of these characteristics relies on their coexistence.

Author (s) Details:

A. V. Monwanou,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

C. H. Miwadinou,
Ecole Normale Sup´erieure de Natitingou, Universit´e d’Abomey, Benin.

C. Ainamon,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

J. B. Chabi Orou,
Institut de Math´ematiques et de Sciences Physiques, Universit´e d’Abomey-Calavi, Benin.

Please see the link here: https://stm.bookpi.org/NRAMCS-V5/article/view/7485

Determination of Correlation and Relative Intensity Noise of the Chaos and the Message Masked by the Chaos | Chapter 4 | New Approaches in Engineering Research Vol. 15

 The promise of secure communication using Chaos is proven analytically in this paper using correlation and Relative Intensity Noise analysis. In pure chaos, auto-correlation coefficients reflect unpredictability, while a correlation coefficient shows a message's decaying periodic nature, which in this case is a sinusoidal signal. Chaos, in both optical and electronic forms, is being studied extensively as a medium for secure communications. The ORIGIN software is used to calculate the correlation coefficient for continuous time delay data and its dependence on time delay. The RIN is calculated for both effectively and inefficiently encoded signals. The RIN for a message that is efficiently encoded is higher than the RIN for a message that is inefficiently encoded. This supports the notion that chaos might be an effective instrument for secure communication.

Author(S) Details

Satyanarayana Chanagala
SBIT, Department of Electronics and Communication, Khammam, Telangana, India.

Madhu Sudhana Rao Kanduri
KKR & KSR Institute of Technology and Sciences, Guntur, Andhrapradesh, India.

View Book:- https://stm.bookpi.org/NAER-V15/article/view/4023

Hydrogen Atom Set up by Electron Capture Describing a Continuous Path | Chapter 3 | New Insights into Physical Science Vol. 12

 In the creation of a hydrogen atom, we present a formulation in which an electron may follow a continuous path. To form electron motion, we use a field Lagrangean basis for chaotic, non-conservative systems. In the case of the proton-nucleus, we discovered electron transition paths ranging from infinity to finite radii, which correspond to stable orbital states. In the chaotic dynamical motion problem, finding these states corresponds to finding the possible stable orbital attractors. Although the electron-proton system has a general collapsing tendency, the Hamiltonian of the system exhibits several metastable states in which the electron will remain for a finite amount of time due to the chaotic perturbations that the electron undergoes during atom forming. The Hamiltonian shifts along the electron course, from zero at infinity to negative values corresponding to certain metastable orbits.

Author (s) Details

D. L. Nascimento
Institute of Physics, University of Brasília, 70919-970 Brasília – DF, Brazil.

A. L. A. Fonseca
Institute of Physics, University of Brasília, 70919-970 Brasília – DF, Brazil and International Center for Condensed Matter, University of Brasília, 70919-970 Brasília – DF, Brazil.

View Book :- https://stm.bookpi.org/NIPS-V12/article/view/281