scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

scholarly journals Spectral properties of magnetohydrodynamic convection with mean horizontal temperature gradient

2006 ◽  
Vol 2 (S239) ◽  
pp. 513-513
Author(s):  
D. Skandera ◽  
W.-Ch. Müller
Keyword(s):  
Temperature Field ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Numerical Code ◽  
Dimensional System ◽  
Horizontal Temperature Gradient ◽  
Mhd Turbulence

AbstractSpectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations (Skandera D. & Müller W.-C. 2006). The investigated system is set up with a mean horizontal temperature gradient in order to avoid a development of elevator instabilities in a fully periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equation are solved by a numerical code (Müller & Biskamp 2000) that uses a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Obtained results are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence (Müller & Biskamp 2000). While the three-dimensional system is found to operate in a Kolmogorov-like regime where buoyant forces have a negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra ∼106), the two-dimensional system exhibits interesting irregular quasi-oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime of turbulence and a standard Iroshnikov-Kraichnan-like regime of turbulence (Müller & Biskamp 2000). The most important parameter determining the turbulent regime of 2D magnetoconvection, apart from a high Rayleigh number, seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer in spectral space. Kinetic, magnetic and temperature energy are transported by a turbulent cascade from large to smaller scales. The local/nonlocal character of the transport is tested for several individual terms in the governing equations. Moreover, other statistical quantities, e.g. probability density functions, are computed as well. A passive character of the temperature field in the investigated three-dimensional magnetoconvection is supported by computations of intermittency using extended self-similarity. The intermittency of the Elsasser field z+ is in agreement with results from numerical simulations of isotropic MHD turbulence (Müller & Biskamp 2000). The intermittency of the temperature field is found to approximately agree with results of passive scalar measurements in hydrodynamic turbulence (Ruiz-Chavarria, Baudet & Ciliberto 1996).

Projective Synchronization of a Modified Coupled Dynamos System

2012 ◽  
Vol 466-467 ◽  
pp. 1261-1265
Author(s):  
Chun Mei Wang ◽  
Ren Long Chang
Keyword(s):  
Chaotic System ◽  
Design Procedure ◽  
Scaling Factor ◽  
Drive System ◽  
Observer Design ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Systematic Design ◽  
Unified Chaotic System ◽  
Placement Technique

Based on techniques from the state observer design and the pole placement technique, we present a systematic design procedure to synchronize a modified coupled dynamos system by a scaling factor ( projective synchronization ). Compared with the method proposed by Wen and Xu, this method eliminates the nonlinear item from the output of the drive system. Furthermore, the scaling factor can be adjusted arbitrarily in due course of control without degrading the controllability. Finally, feasibility of the technique is illustrated for the unified chaotic system.

PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350113 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Drive System ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Response System ◽  
Opposite Situation ◽  
The One ◽  
Hyperchaotic Systems

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

Adaptive Projective Synchronization of the New Three-Dimensional Chaotic System

2013 ◽  
Vol 321-324 ◽  
pp. 921-924 ◽  
Author(s):  
Su Hai Huang
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Synchronization ◽  
Three Dimensional ◽  
Projective Synchronization ◽  
Time Stability ◽  
Finite Time Stability ◽  
Adaptive Technique ◽  
New Chaotic System ◽  
Synchronization Scheme

This paper deals with the finite-time chaos synchronization of the new chaotic system [with uncertain parameters. Based on the finite-time stability theory and adaptive technique, a controller has been designed to realize finite-time chaos projective synchronization and parameter identification. Moreover, numerical simulation result is included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

scholarly journals Application of Theory to Simulations of Observed Cases of Orographically Forced Convective Rainfall

2012 ◽  
Vol 140 (9) ◽  
pp. 3039-3053 ◽  
Author(s):  
Mario Marcello Miglietta ◽  
Richard Rotunno
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Wind Component ◽  
Convective Rainfall ◽  
Simulated Precipitation ◽  
Cloud Resolving Model ◽  
Simulated Rain ◽  
Wind Profiles ◽  
Rain Rates

Abstract In two recent papers, the authors reported on numerical simulations of conditionally unstable flows past an idealized mesoscale mountain ridge. These idealized simulations, which were performed with a three-dimensional, explicitly cloud-resolving model, allowed the investigation of simulated precipitation characteristics as a function of the prescribed environment. The numerical solutions were carried out for a uniform wind flowing past a bell-shaped ridge and using an idealized unstable sounding with prescribed values of the relevant parameters. In the present work the application of these theoretical results to observed cases of orographically forced convective rainfall including the Big Thompson flood (1976, Colorado), the Oahu flood (1974, Hawaii), and the Gard flood (2002, France) is reported. Specifically, numerical simulations have been carried out using observed and idealized soundings relevant to these cases but with idealized topography. It is found that using the observed soundings, but with idealized constant-wind profiles, the simulated rain rates fit reasonably well within the previous theoretically derived parameter space for intense orographic convective rainfall. However, in order to reproduce larger rainfall rates, in closer agreement with observations, in the first two cases it was necessary to initialize the sounding with a wind profile characterized by low-level flow toward the mountain with weak flow aloft (as observed for the across-mountain wind component). For the Gard case, the situation was more complex and it is found unlikely that the situation can be reduced to a simple two-dimensional problem.

scholarly journals One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order1

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhou ◽  
Rongji Bai
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Result ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Lorenz Chaotic System

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in1<q<2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order1<q<2is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

scholarly journals Numerical Simulations of Conditionally Unstable Flows over a Mountain Ridge

2009 ◽  
Vol 66 (7) ◽  
pp. 1865-1885 ◽  
Author(s):  
Mario Marcello Miglietta ◽  
Richard Rotunno
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Cloud Model ◽  
Three Dimensional ◽  
Cold Pool ◽  
Density Currents ◽  
Mountain Ridge ◽  
Wind Speeds ◽  
Wind Profiles ◽  
Convective Cells

Abstract Numerical simulations of conditionally unstable flows impinging on a mesoscale mountain ridge have been performed with an explicitly resolving cloud model to investigate the statistically stationary features of the solution precipitation characteristics. The simulations are performed on a three-dimensional domain and at high resolution (grid spacing: 250 m) to properly resolve cellular-scale features. Although the environmental conditions are specified by a simplified idealized conditionally unstable sounding, there are still quite a few external parameters, so only a limited portion of the parameter space was explored. Numerical solutions were first carried out for different uniform-wind profiles impinging on a bell-shaped ridge 2000 m high. In the experiments with weaker environmental wind speeds (2.5 m s−1), the cold-air outflow, caused by the evaporative cooling of rain from precipitating convective cells, is the main mechanism for cell redevelopment and movement; this outflow produces new convective cells near the head of the up- and downstream density currents, which rapidly propagate far from the ridge so that no rainfall is produced close to the ridge at later times. For larger wind speeds (10 and 20 m s−1), there is less time for upwind, evaporation-induced cold-pool formation before air parcels reach the ridge top and descend downwind. For the intermediate wind speed (10 m s−1), evaporation is effective in generating a cold pool only on the downstream side of the ridge, in a region where the air is unsaturated and slow moving. Further experiments with different ridge heights and half-widths were carried out in order to analyze their effect on the distribution and intensity of precipitation. Dimensional analysis reveals that the maximum (nondimensional) rainfall rate mainly depends on the ratio of mountain height to the level of free convection, the ridge aspect ratio, and a parameter that measures the ratio of advective to convective time scales.

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