Marius-F. Danca


BOOKS

Functia logistica: dinamica, bifurcatie si haos

(in Romanian)

Seria MATEMATICA APLICATA SI INDUSTRIALA 7

Editura Universitatii din Pitesti, 2001

Special Issue

Stability, Periodicity, and Related Problems in Fractional-Order Systems

2022

A special issue of Mathematics (ISSN 2227-7390). "Engineering Mathematics".

Editors: Mickal Feckan

and

Marius-F. Danca

 

Sisteme dinamice discontinue

(in Romanian)

Seria MATEMATICA APLICATA SI INDUSTRIALA 14

Editura Universitatii din Pitesti, 2004

Chapter:

Chaos Control and Anticontrol of Complex Systems via Parrondo’s Game

in

Complex Systems and Networks,

Dynamics, Controls and Applications

Understanding Complex Systems, 2016

Springer, ISBN 978-3-662-47824-0

 

Special issue

"Bifurcation and
Chaos in Fractional-
Order Systems
"

MDPI (Symmetry)

2021

ISBN 978-3-0365-0092-8 (Hbk); ISBN 978-3-0365-0093-5 (PDF)
https://doi.org/10.3390/books978-3-0365-0093-5

Editors
Marius-F. Danca
Guanrong Chen

Special issue

"Research Frontier in Chaos Theory and Complex Networks"

MDPI (Entropy)

2018

(ISSN 1099-4300)

Editors
Guanrong Chen
Marius-F. Danca
Xiaosong Yang
Genaro J. Martinez
Hai Yu

 

Cuprins

Notatii si concepte
1 Scurt istoric
2 Bifurcatia furcã si drumul spre haos al dublãrilor perioadei
3 Bifurcatia tangentã
4 Calculul numãrului de orbite de perioadã p
4.1 Formula lui Metropolis, Stein si Stein
4.2 Formula lui Weiss si Rogers
5 Polinoame critice
6 Atractorii functiei logistice
7 Dimensiuni
8 Dependenta iteratelor de parametrul r
8.1 Regimul periodic
8.2 Regimul haotic
9 Mãsurã si ergodicitate
10 Exponentii Lyapunov
11 Entropie
12 Bifurcatie si universalitate
13 Supercicluri
14 Transformarea de dublare si constanta a
15 Transformarea liniarizatã de dublare si constanta d

16 Fenomenul de intermitentã
17 Utilizarea grupului de renormalizare în studiul intermitentei
18 Crize si haos tranzitoriu
18.1 Crizele de frontierã si haosul tranzitoriu
18.2 Intermitenta indusã de crize
19 Dinamicã simbolicã aplicatã
19.1 Teorema lui Metropolis, Stein si Stein
19.2 Produsul sirurilor de simboluri ale unei functii de tip logistic
19.3 Ordonarea sirurilor la o functie de tip logistic
19.4 Paterne ale orbitelor superstabile de primã si ultimã aparitie
19.5 Calculul parametrului unei orbite superstabile; formula lui Kaplan
19.6 Ordonarea orbitelor periodice; teorema lui Sharkovsky
19.7 Functia de siftare
20 Haos si determinism
21 Controlul haosului
21.1 Algoritmul OGY
21.2 Algoritmul GM
22 Anticontrolul haosului
23 Sincronizarea orbitelor haotice
24 Functia logisticã si multimile fractale Julia si Mandelbrot
24.1 Generarea multimilor Julia
24.2 Generarea multimii Mandelbrot

Anexe
1: Stabilitate si atractivitate
2: Tipuri de bifurcatii
3: Preperioadã si puncte Misiurewicz
4: Dimensiuni
5: Exponentii Lyapunov
6: Teorema lui Sharkovsky
7: Atractori haotici (stranii)
8: Functia cort
9: Haos în sensul lui Li si Yorke
10:Multimile Julia si Mandelbrot
11: Spectrul de putere
12: Programe utilizate pentru simulare

Bibliografie

Index


"Desi studiul sistematic al functiei logistice începe odatã cu lucrãrile lui Fiegenbaum de la jumãtatea anilor ’70 si continuã cu foarte multe altele, pe care revistele din strãinãtate le reflectã cu generozitate, în tara noastrã, pânã acum nu a apãrut o monografie dedicatã acestei functii. Publicul român n-a beneficiat de o lucrare apãrutã în tarã prin care el sã ia cunostintã de acest subiect, fierbinte peste hotare, obligator si atât de formativ pentru cercetãtorul si practicianul de azi si de mâine. De aceea, cu o mare bucurie am subscris la prezenøa acestei utile cãrti în seria noastrã de matematicã aplicatã si industrialã."

10 Ianuarie 2001, Bucuresti,

Prof. Adelina Georgescu,
Facultatea de Matematica,
Universitatea din Pitesti,
Romania

 

Cuprins

Introducere
1 Sisteme dinamice switch

1.0 Notatii si concepte de sisteme dinamice
1.1 Problema de valori initiale
1.2 Existenta solutiilor
1.3 Unicitatea solutiilor
1.4 Sisteme dinamice switch

2 Aproximarea sistemelor dinamice switch
2.1 Metoda lui Euler pentru incluziuni diferentiale si aplicatii ale ei
2.2 Aproximarea prin metoda lui Euler generatoare a unui sistem dinamic switch
2.3 Aproximarea sistemelor dinamice switch cu ajutorul Teoremei lui Cellina

3 Anticontrolul sistemelor dinamice switch
3.1 Algoritmul de anticontrol pentru cazul sistemelor dinamice continue
-Anticontrolul haosului într-o ecuatie diferentialã liniarã stabilã
-Anticontrolul haosului într-un sistem liniar stabil
-Anticontrolul haosului în ecuatii diferentiale neliniare stabile
-Anticontrolul haosului în sisteme afine neliniare stabile
3.2 Algoritmul de anticontrol al sistemelor dinamice switch
-Derivata generalizatã a functiilor de clasã M
-Anticontrolul sistemelor dinamice switch

4 Sincronizarea sistemelor dinamice switch
4.1 Exponen¡ii Lyapunov pentru sisteme dinamice switch
4.2 Sincronizarea sistemelor dinamice switch

Anexe
A Functii multivoce: notiuni si rezultate auxiliare
B Schema bloc a circuitului switch al lui Chua
C Determinarea selectiei aproximante pentru sistemul lui Chua
D Notiuni de stabilitate a unui sistem dinamic
E Tipuri de bifurcatii
-Bifurcatia furcã
-Bifurcatia tangentã si bifurcatia sa-nod
-Bifurcatia Hopf
F Exponentii Lyapunov pentru sisteme dinamice netede
G Atractori haotici
H Haos în sensul Li si Yorke; Teorema lui Marotto
I Aplicatia lui Poincaré
J Dinamica unui sistem dinamic switch pe suprafata de discontinuitate
K Fenomenul stick-slip

Bibliografie

Index


"Apart from Filippov’s theory, there are two monographs which have advanced the understanding of dynamical systems with discontinuities. The first is Non-smooth Dynamical Systems by Marcus Kunze, which gives solid background, however it is quite short on providing a number of convincing examples. The second book entitled Applied Nonlinear Dynamics of Mechanical Systems with Discontinuities edited by Wiercigroch and de Kraker, gives numerous examples how such systems can be solved. This leaves the literate of discontinuous dynamical systems seriously short and every effort to improve status quo is very welcome. The monograph by Marius Danca Sisteme dinamice discontinue fills the gap between the two above works, and would be instrumental in stimulating the field of discontinuous dynamical systems in Romania, and hopefully if translated to English, an extremely useful addition to the existing literature."

 

January 2004

Prof. Marian Wiercigroch
Director of Centre for Applied Dynamics Research
University of Aberdeen, UK


Table of contents


1. Discovering Cluster Dynamics Using Kernel Spectral Methods Langone, Rocco (et al.)

2. Community Detection in Bipartite Networks: Algorithms and Case studies Alzahrani, Taher (et al.)

3. Epidemiological Modeling on Complex Networks 4.Jin, Zhen (et al.)

4. Resilience of Spatial Networks, Li, Daqing

5. Synchronization and Control of Hyper-Networks and Colored Networks, Fu, Xinchu (et al.)

6. New Nonlinear CPRNG Based on Tent and Logistic Maps, Garasym, Oleg (et al.)

7. Distributed Finite-Time Cooperative Control of Multi-agent Systems, Zhao, Yu (et al.)

8. Composite Finite-Time Containment Control for Disturbed Second-Order Multi-agent Systems, Wang, Xiangyu (et al.)

9. Application of Fractional-Order Calculus in a Class of Multi-agent Systems, Yu, Wenwu (et al.)


10. Chaos Control and Anticontrol of Complex Systems via Parrondo’s Game, Danca, Marius-F.

11. Collective Behavior Coordination with Predictive Mechanisms, Zhang, Hai-Tao (et al.)

12. Convergence, Consensus and Synchronization of Complex Networks via Contraction Theory, di Bernardo, Mario (et al.)

13. Towards Structural Controllability of Temporal Complex Networks, Li, Xiang (et al.)

14. A General Model for Studying Time Evolution of Transition Networks, Zhan, Choujun (et al.)

15. Deflection Routing in Complex Networks, Haeri, Soroush (et al.)

16. Recommender Systems for Social Networks Analysis and Mining: Precision Versus Diversity, Javari, Amin (et al.)

17. Strategy Selection in Networked Evolutionary Games: Structural Effect and the Evolution of Cooperation, Tan, Shaolin (et al.)

18. Network Analysis, Integration and Methods in Computational Biology: A Brief Survey on Recent Advances, Zhang, Shihua

"Nowadays, networks exist everywhere. In the recent decade, complex networks have been widely investigated partly due to their wide applications in biological neural networks, ecosystems, metabolic pathways, the Internet, the WWW, electrical power grids, communication systems, etc., and partly due to their broad scientific progress in physics, mathematics, engineering, biology, etc. The key character for a complex network is that it can represent a large-scale system in
nature, human societies, and technology with the nodes representing the individual agents and the edges representing the mutual connections. Thus, the research work on fundamental properties, such as dynamics, controls, and applications of various complex networks has become overwhelming recently. Actually, complex network studies can be dated back to the eighteenth century when the great mathematician Leonhard Euler studied the well-known Königsburg seven-bridge problem. Then, in the early 1960s, Erdös and Rényi (ER) proposed a random-graph model, which can be regarded as the modern network theory framework. In order to describe a transition from a regular network to a random network, Watts and Strogatz (WS) rewired the connections on some nodes in a
regular network and proposed a small-world network model. Then, Barabási and Albert (BA) proposed a new scale-free network model, in which the degree distribution of the nodes follows a power-law form. Thereafter, complex networks
have been widely discussed. In particular, small-world and scale-free complex networks have been extensively investigated worldwide.
The contents of this book are summarized as follows. First, the dynamics of complex networks are studied regarding, for example, the cluster dynamic analysis using kernel spectral methods, community detection algorithms in bipartite networks, epidemiological modeling with demographics and epidemic spreading on multi-layer networks, and resilience of spatial networks leading to the catastrophic cascading failures under various local perturbations. Then, some evolving hyper-network and color-network models are generated by adopting both growth and preferential attachment mechanisms and some new nonlinear chaotic pseudo random number generator, based on tent and logistic maps are also discussed.
Second, the controls of complex networks are investigated. The interesting topics include distributed finite-time cooperative control of multi-agent systems by applying homogeneous-degree and Lyapunov methods, composite finite-time containment control for disturbed second-order multi-agent systems, fractional-order observer design of multi-agent systems, chaos control and anticontrol of complex systems via Parrondos game, collective behavior coordination
with predictive mechanisms, convergence, consensus and synchronization of complex networks via contraction theory, and structural controllability of temporal complex networks.
Third, the applications of complex networks provide some applicable carriers, which show the importance of theories developed in complex networks. In particular, a general model for studying time evolution of transition networks,
deflection routing in complex networks, recommender systems for social networks analysis and mining, strategy selection in networked evolutionary games, integration and methods in computational biology, are discussed in detail.
Recently, studies of the dynamics and controls of complex networks have become more attractive. In particular, some emergent behaviors of complex networks need to be investigated because new applied science and technology require new methods and theories to solve new challenging problems. Thus, an in-depth study with detailed description of dynamics, controls, and applications of complex
networks will benefit both theoretical research and applications in the near-future development of related subjects. This book provides some state-of-the-art research
results on broad disciplinary sciences in complex networks to meet such demands.
We would like to express our sincere thanks to all the chapter contributors for their great support to our book, without which this book would not have been possible. Special thanks are directed to the founding editor of the Springer Series in
Understanding Complex Systems, Scott Kelso, for his encouragement and support to edit this volume. Thanks also go to Dr. Thomas Ditzinger, Holger Schäpe, and Priyadarshini Senthilkumar from Springer for their assistance during the publication of this book. Last but not least, we also would like to thank the financial support from the National Science and Technology Major Project of China under Grant
2014ZX10004001-014, the 973 Project under Grant 2014CB845302, and the National Natural Science Foundation of China under Grant Nos. 11472290,
61322302, and 61104145, Australian Research Council Discovery under Grants Nos. DP130104765 and DP140100544, and Hong Kong Research Grants Council
under the G RF Grants CityU 11201414 and 11208515.
Beijing "

Jinhu Lü
Xinghuo Yu
Guanrong Chen
Wenwu Yu

May 2015

Contents


About the Editors . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . vii
Preface to ”Bifurcation and Chaos
in Fractional-Order Systems” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Ant´onio M. Lopes, J. A. Tenreiro Machado
Fractional Dynamics in Soccer Leagues........... . . . . . . . . . . . . . . . . 1
Marius-F. Danca
Puu System of Fractional Order and Its Chaos Suppression. . . . . . . 13
Shao Fu Wang and Aiqin Ye
Dynamical Properties of Fractional-Order Memristor . . . . . . . . . . 25
Shouwu Duan, Wanqing Song, Carlo Cattani, Yakufu Yasen and He Liu
Fractional Levy Stable and Maximum Lyapunov Exponent for Wind Speed Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 37
Fatima Hadjabi, Adel Ouannas, Nabil Shawagfeh, Amina-Aicha Khennaoui and Giuseppe Grassi
On Two-Dimensional Fractional Chaotic Maps with Symmetries . . 51
Adel Ouannas, Othman Abdullah Almatroud, Amina Aicha Khennaoui, Mohammad Mossa Alsawalha, Dumitru Baleanu, Van Van Huynh, Viet-Thanh Pham
Bifurcations, Hidden Chaos and Control in Fractional Maps . . . . . . 65
Mohammad Izadi and Carlo Cattani
Generalized Bessel Polynomial for Multi-Order Fractional Differential Equations

 

In recent years, as natural and social sciences are rapidly evolving, classical chaos theoryand modern complex networks studies are gradually interacting each other with a great joineddevelopment. In particular, the notion of complex networks is becoming a self-contained interdiscipline.Network science as a whole has merged with the basic research and real-world applications of chaostheory, forming one of the most active fields in cognitive science, data science, cloud computing,social sciences, artificial intelligence, and the like.The theme of this special Issue is on the current research efforts and progress in the promisingfield of chaos theory as well as complex networks. It comprises 17 selected manuscripts primarilyinvolving four types of subjects, namely theoretical and characteristic analysis of chaotic dynamics,control systems and synchronization, complex networks, and chaos-based applications.