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Bekiros S, Jahanshahi H, Munoz-Pacheco JM. A new buffering theory of social support and psychological stress. PLoS One 2022; 17:e0275364. [PMID: 36223401 PMCID: PMC9555651 DOI: 10.1371/journal.pone.0275364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 09/15/2022] [Indexed: 11/06/2022] Open
Abstract
A dynamical model linking stress, social support, and health has been recently proposed and numerically analyzed from a classical point of view of integer-order calculus. Although interesting observations have been obtained in this way, the present work conducts a fractional-order analysis of that model. Under a periodic forcing of an environmental stress variable, the perceived stress has been analyzed through bifurcation diagrams and two well-known metrics of entropy and complexity, such as spectral entropy and C0 complexity. The results obtained by numerical simulations have shown novel insights into how stress evolves with frequency and amplitude of the perturbation, as well as with initial conditions for the system variables. More precisely, it has been observed that stress can alternate between chaos, periodic oscillations, and stable behaviors as the fractional order varies. Moreover, the perturbation frequency has revealed a narrow interval for the chaotic oscillations, while its amplitude may present different values indicating a low sensitivity regarding chaos generation. Also, the perceived stress has been noted to be highly sensitive to initial conditions for the symptoms of stress-related ill-health and for the social support received from family and friends. This work opens new directions of research whereby fractional calculus might offer more insight into psychology, life sciences, mental disorders, and stress-free well-being.
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Affiliation(s)
- Stelios Bekiros
- LSE Health Centre & Department of Health Policy, London School of Economics and Political Science (LSE), London, United Kingdom
- Faculty of Economics &Management (FEMA), University of Malta, Msida, Malta
- * E-mail: , ,
| | - Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada
| | - Jesus M. Munoz-Pacheco
- Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
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Morales-Centla N, Torrealba-Melendez R, Tamariz-Flores EI, López-López M, Arriaga-Arriaga CA, Munoz-Pacheco JM, Gonzalez-Diaz VR. Dual-Band CPW Graphene Antenna for Smart Cities and IoT Applications. Sensors (Basel) 2022; 22:5634. [PMID: 35957191 PMCID: PMC9371184 DOI: 10.3390/s22155634] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 07/21/2022] [Accepted: 07/27/2022] [Indexed: 06/15/2023]
Abstract
In this paper, a dual-band graphene coplanar waveguide antenna is designed for smart cities and internet of things applications. A graphene film is chosen as the conductive material for the radiation patches and ground plane with a thickness of 240 μm and an electric conductivity of 3.5 × 105 S/m. The dielectric is glass with a dielectric permittivity of 6 and a thickness of 2 mm. The implementation of the antenna on glass permits the integration of the antenna in smart cities and IoT applications. This antenna is based on two trapezoidal patches that generate the dual-band behavior. The overall dimensions of the antenna are 30 mm × 30 mm × 2 mm. The reflection coefficient, gain, and radiation patterns were measured and compared with the simulations. The antenna covers two frequency bands; the lower band covers the 2.45 GHz ISM band, and the upper band range covers from 4 to 7 GHz.
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Affiliation(s)
- Nathaniel Morales-Centla
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
| | - Richard Torrealba-Melendez
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
| | | | - Mario López-López
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
| | - Cesar Augusto Arriaga-Arriaga
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
| | - Jesus M. Munoz-Pacheco
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
| | - Victor R. Gonzalez-Diaz
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico; (N.M.-C.); (M.L.-L.); (C.A.A.-A.); (J.M.M.-P.); (V.R.G.-D.)
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Munoz-Pacheco JM, Volos C, Serrano FE, Jafari S, Kengne J, Rajagopal K. Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique. Entropy (Basel) 2021; 23:e23070921. [PMID: 34356462 PMCID: PMC8306190 DOI: 10.3390/e23070921] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2021] [Revised: 07/10/2021] [Accepted: 07/15/2021] [Indexed: 12/04/2022]
Abstract
In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.
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Affiliation(s)
- Jesus M. Munoz-Pacheco
- Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico
- Correspondence:
| | - Christos Volos
- Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;
| | - Fernando E. Serrano
- Instituto de Investigacion en Energia IIE, Universidad Nacional Autonoma de Honduras (UNAH), Tegucigalpa 11101, Honduras; or
| | - Sajad Jafari
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam;
| | - Jacques Kengne
- Department of Electrical Engineering, University of Dschang, Dschang P.O. Box 134, Cameroon;
| | - Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India; or
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Jahanshahi H, Munoz-Pacheco JM, Bekiros S, Alotaibi ND. A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19. Chaos Solitons Fractals 2021; 143:110632. [PMID: 33519121 PMCID: PMC7832492 DOI: 10.1016/j.chaos.2020.110632] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 12/23/2020] [Accepted: 12/25/2020] [Indexed: 05/04/2023]
Abstract
COVID-19 is a novel coronavirus affecting all the world since December last year. Up to date, the spread of the outbreak continues to complicate our lives, and therefore, several research efforts from many scientific areas are proposed. Among them, mathematical models are an excellent way to understand and predict the epidemic outbreaks evolution to some extent. Due to the COVID-19 may be modeled as a non-Markovian process that follows power-law scaling features, we present a fractional-order SIRD (Susceptible-Infected-Recovered-Dead) model based on the Caputo derivative for incorporating the memory effects (long and short) in the outbreak progress. Additionally, we analyze the experimental time series of 23 countries using fractal formalism. Like previous works, we identify that the COVID-19 evolution shows various power-law exponents (no just a single one) and share some universality among geographical regions. Hence, we incorporate numerous memory indexes in the proposed model, i.e., distinct fractional-orders defined by a time-dependent function that permits us to set specific memory contributions during the evolution. This allows controlling the memory effects of more early states, e.g., before and after a quarantine decree, which could be less relevant than the contribution of more recent ones on the current state of the SIRD system. We also prove our model with Italy's real data from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University.
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Affiliation(s)
- Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg R3T 5V6, Canada
| | - Jesus M Munoz-Pacheco
- Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, 72570 Mexico
| | - Stelios Bekiros
- European University Institute, Department of Economics, Via delle Fontanelle, 18, Florence, I-50014, Italy
- Rimini Centre for Economic Analysis (RCEA), LH3079, Wilfrid Laurier University, 75 University Ave W., ON Waterloo, N2L3C5, Canada
| | - Naif D Alotaibi
- Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
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Volos CK, Jafari S, Munoz-Pacheco JM, Kengne J, Rajagopal K. Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II. Entropy (Basel) 2020; 22:e22121428. [PMID: 33352853 PMCID: PMC7767120 DOI: 10.3390/e22121428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Accepted: 12/15/2020] [Indexed: 06/12/2023]
Abstract
According to the pioneering work of Leonov and Kuznetsov [...].
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Affiliation(s)
- Christos K. Volos
- Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
| | - Sajad Jafari
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam;
| | | | - Jacques Kengne
- Department of Electrical Engineering, University of Dschang, P.O. Box 134 Dschang, Cameroon;
| | - Karthikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India; or
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Wang S, Yousefpour A, Yusuf A, Jahanshahi H, Alcaraz R, He S, Munoz-Pacheco JM. Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method. Entropy (Basel) 2020; 22:e22030271. [PMID: 33286045 PMCID: PMC7516724 DOI: 10.3390/e22030271] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Revised: 02/23/2020] [Accepted: 02/24/2020] [Indexed: 11/20/2022]
Abstract
In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.
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Affiliation(s)
- Shaojie Wang
- College of Electrical and Information Engineering, Shaoyang University, Shaoyang 422000, China;
| | - Amin Yousefpour
- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran 11155-4563, Iran;
| | - Abdullahi Yusuf
- Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey;
- Department of Mathematics, Federal University Dutse, Jigawa 7156, Nigeria
| | - Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada;
| | - Raúl Alcaraz
- Research Group in Electronic, Biomedical and Telecommunication Engineering, University of Castilla-La Mancha, 16071 Cuenca, Spain
- Correspondence:
| | - Shaobo He
- School of Physics and Electronics, Central South University, Changsha 410083, China;
| | - Jesus M. Munoz-Pacheco
- Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, Mexico 72570, Mexico;
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Jahanshahi H, Yousefpour A, Munoz-Pacheco JM, Moroz I, Wei Z, Castillo O. A new multi-stable fractional-order four-dimensional system with self-excited and hidden chaotic attractors: Dynamic analysis and adaptive synchronization using a novel fuzzy adaptive sliding mode control method. Appl Soft Comput 2020. [DOI: 10.1016/j.asoc.2019.105943] [Citation(s) in RCA: 97] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Volos CK, Jafari S, Kengne J, Munoz-Pacheco JM, Rajagopal K. Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors. Entropy (Basel) 2019; 21:e21040370. [PMID: 33267084 PMCID: PMC7514854 DOI: 10.3390/e21040370] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 04/03/2019] [Indexed: 01/09/2023]
Affiliation(s)
- Christos K. Volos
- Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
- Correspondence:
| | - Sajad Jafari
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
| | - Jacques Kengne
- Department of Electrical Engineering, University of Dschang, P.O. Box 134 Dschang, Cameroon
| | | | - Karthikeyan Rajagopal
- Center for Nonlinear Dynamics, Institute of Research and Development, Defence University, P.O. Box 1041 Bishoftu, Ethiopia
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Munoz-Pacheco JM, Zambrano-Serrano E, Volos C, Jafari S, Kengne J, Rajagopal K. A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors. Entropy (Basel) 2018; 20:e20080564. [PMID: 33265653 PMCID: PMC7513089 DOI: 10.3390/e20080564] [Citation(s) in RCA: 57] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2018] [Revised: 07/23/2018] [Accepted: 07/25/2018] [Indexed: 12/03/2022]
Abstract
In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a ‘hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.
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Affiliation(s)
- Jesus M. Munoz-Pacheco
- Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico
- Correspondence: ; Tel.: +52-222-229-5500
| | | | - Christos Volos
- Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran
| | - Jacques Kengne
- Department of Electrical Engineering, University of Dschang, P.O. Box 134 Dschang, Cameroon
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