scholarly journals Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Ngo Mouelas Adele ◽  
Kammogne Soup Tewa Alain ◽  
Romanic Kengne ◽  
Fotsin Hilaire Bertrand
Keyword(s):  
Time Synchronization ◽  
Initial Conditions ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Multiple Attractors ◽  
Function Projective Synchronization ◽  
Wide Range ◽  
Coupling Path ◽  
Two Parameters ◽  
And Function

Regions of stability phases discovered in a general class of Genesio−Tesi chaotic oscillators are proposed. In a relatively large region of two-parameter space, the system has coexisting point attractors and limit cycles. The variation of two parameters is used to characterize the multistability by plotting the isospike diagrams for two nonsymmetric initial conditions. The parameters window in which the jerk system exhibits the unusual and striking feature of multiple attractors (e.g., coexistence of six disconnected periodic chaotic attractors and three-point attraction) is investigated. The second aspect of this study presents the synchronization of systems that act as mediators between two dynamical units that, in turn, show function projective synchronization (FPS) with each other. These are the so-called relay systems. In a wide range of operating parameters; this setup leads to synchronization between the outer circuits, while the relaying element remains unsynchronized. The results show that the coupled systems can achieve function projective synchronization in a determined time despite the unpredictability of the scaling function. In the coupling path, the outer dynamical systems show finite-time synchronization of their outputs, that is, displaying the same dynamics at exactly the same moment. Further, this effect is rather general and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.

Multistability and Bubbling Route to Chaos in a Deterministic Model for Geomagnetic Field Reversals

2019 ◽  
Vol 29 (12) ◽  
pp. 1930034
Author(s):  
Paulo C. Rech ◽  
Sudarshan Dhua ◽  
N. C. Pati
Keyword(s):  
Fixed Point ◽  
Geomagnetic Field ◽  
Deterministic Model ◽  
Initial Conditions ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Multiple Attractors ◽  
System A ◽  
Two Parameters

We report coexisting multiple attractors and birth of chaos via period-bubbling cascades in a model of geomagnetic field reversals. The model system comprises a set of three coupled first-order quadratic nonlinear equations with three control parameters. Up to seven kinds of multistable attractors, viz. fixed point-periodic, fixed point-chaotic, periodic–periodic, periodic-chaotic, chaotic–chaotic, fixed point-periodic–periodic, fixed point-periodic-chaotic are obtained depending on the initial conditions for critical parameter sets. Antimonotonicity is a striking characteristic feature of nonlinear systems through which a full Feigenbaum tree corresponding to creation and annihilation of period-doubling cascades is developed. By analyzing the two-parameters dependent dynamics of the system, a critical biparameter zone is identified, where antimonotonicity comes into existence. The complex dynamical behaviors of the system are explored using phase portraits, bifurcation diagrams, Lyapunov exponents, isoperiodic diagram, and basins of attraction.

scholarly journals Predefined-Time Modified Function Projective Synchronization for Multiscroll Chaotic Systems via Sliding Mode Control Technology

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qiaoping Li ◽  
Chao Yue
Keyword(s):  
Sliding Mode Control ◽  
Time Synchronization ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Control Technology ◽  
Function Projective Synchronization ◽  
Mode Control ◽  
Modified Function Projective Synchronization ◽  
Error System

In the context of chaotic secure communication and based on the sliding mode control technology, this article investigates the predefined-time modified function projective synchronization for the Colpitts oscillator multiscroll hyperchaotic systems. Firstly, a four-dimensional multiscroll hyperchaotic system is introduced and the predefined-time synchronization is defined. Subsequently, applying a novel predefined-time stability criterion, an integral terminal sliding mode surface is constructed for the synchronization error system to ensure that the sliding motion is stable within a predefined time; meanwhile, an approaching controller is designed to enable the error system to reach and remain on the sliding mode surface within another predefined time, so as to ensure the realization of the predefined-time synchronization. Finally, the simulation experiments are presented to verify the effectiveness of derived theoretical results.

scholarly journals A New 4D Hyperchaotic System and Its Generalized Function Projective Synchronization

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yuan Gao ◽  
Chenghua Liang
Keyword(s):  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Generalized Function ◽  
Hyperchaotic System ◽  
Function Projective Synchronization ◽  
And Function ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Generalized Function Projective Synchronization ◽  
New System

A new four-dimensional hyperchaotic system is investigated. Numerical and analytical studies are carried out on its basic dynamical properties, such as equilibrium point, Lyapunov exponents, Poincaré maps, and chaotic dynamical behaviors. We verify the realizability of the new system via an electronic circuit by using Multisim software. Furthermore, a generalized function projective synchronization scheme of two different hyperchaotic systems with uncertain parameters is proposed, which includes some existing projective synchronization schemes, such as generalized projection synchronization and function projective synchronization. Based on the Lyapunov stability theory, a controller with parameters update laws is designed to realize synchronization. Using this controller, we realize the synchronization between Chen hyperchaotic system and the new system to verify the validity and feasibility of our method.

Chaperonin as the normal controls and pathological anti-stress response in the human reproductive system

2016 ◽  
pp. 126-129
Author(s):  
M. Makarenko ◽  
◽  
D. Hovsyeyev ◽  
L. Sydoryk ◽  
◽  
...  
Keyword(s):  
Reproductive System ◽  
Stress Proteins ◽  
Physiological Stress ◽  
Protein Complexes ◽  
Reproductive Function ◽  
Intercellular Signaling ◽  
Toll Like Receptors ◽  
Wide Range ◽  
Protein Functions ◽  
And Function

Different kinds of physiological stress cause mass changes in the cells, including the changes in the structure and function of the protein complexes and in separate molecules. The protein functions is determined by its folding (the spatial conclusion), which depends on the functioning of proteins of thermal shock- molecular chaperons (HSPs) or depends on the stress proteins, that are high-conservative; specialized proteins that are responsible for the correct proteinaceous folding. The family of the molecular chaperones/ chaperonins/ Hsp60 has a special place due to the its unique properties of activating the signaling cascades through the system of Toll-like receptors; it also stimulates the cells to produce anti- inflammatory cytokines, defensins, molecules of cell adhesion and the molecules of MHC; it functions as the intercellular signaling molecule. The pathological role of Hsp60 is established in a wide range of illnesses, from diabetes to atherosclerosis, where Hsp60 takes part in the regulation of both apoptosis and the autoimmune processes. The presence of the HSPs was found in different tissues that are related to the reproductive system. Key words: molecular chaperons (HSPs), Toll-like receptors, reproductive function, natural auto antibody.

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