Control of amplitude death by coupling range in a network of fractional-order oscillators

2020 ◽  
Vol 34 (31) ◽  
pp. 2050303
Author(s):  
Rui Xiao ◽  
Zhongkui Sun
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Coupling Strength ◽  
Low Frequency ◽  
System Size ◽  
Coupled Systems ◽  
Amplitude Death ◽  
Function Relationship ◽  
The Relationship

We investigate the oscillating dynamics in a ring of network of nonlocally delay-coupled fractional-order Stuart-Landau oscillators. It is concluded that with the increasing of coupling range, the structures of death islands go from richness to simplistic, nevertheless, the area of amplitude death (AD) state is expanded along coupling delay and coupling strength directions. The increased coupling range can prompt the coupled systems with low frequency to occur AD. When system size varies, the area of death islands changes periodically, and the linear function relationship between periodic length and coupling range can be deduced. Thus, one can modulate the oscillating dynamics by adjusting the relationship between coupling range and system size. Furthermore, the results of numerical simulations are consistent with theoretical analysis.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

Relationship between negative differential thermal resistance and asymmetry segment size

2018 ◽  
Vol 32 (07) ◽  
pp. 1850079 ◽  
Author(s):  
Peng Kong ◽  
Tao Hu ◽  
Ke Hu ◽  
Zhenhua Jiang ◽  
Yi Tang
Keyword(s):  
Thermal Resistance ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
System Size ◽  
Coupling Constant ◽  
Interface Coupling ◽  
Segment Size

Negative differential thermal resistance (NDTR) was investigated in a system consisting of two dissimilar anharmonic lattices exemplified by Frenkel–Kontorova (FK) lattices and Fremi–Pasta–Ulam (FPU) lattices (FK-FPU). The previous theoretical and numerical simulations show the dependence of NDTR are the coupling constant, interface and system size, but we find the segment size also to be an important element. It’s interesting that NDTR region depends on FK segment size rather than FPU segment size in this coupling FK-FPU model. Remarkably, we could observe that NDTR appears in the strong interface coupling strength case which is not NDTR in previous studies. The results are conducive to further developments in designing and fabricating thermal devices.

scholarly journals Harmonic Balance Method for Chaotic Dynamics in Fractional-Order Rössler Toroidal System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Huijian Zhu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Chaotic Motions ◽  
Behavior Based

This paper deals with the problem of determining the conditions under which fractional order Rössler toroidal system can give rise to chaotic behavior. Based on the harmonic balance method, four detailed steps are presented for predicting the existence and the location of chaotic motions. Numerical simulations are performed to verify the theoretical analysis by straightforward computations.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

scholarly journals Analysis of two- and three-dimensional fractional-order Hindmarsh-Rose type neuronal models

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Eva Kaslik
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Three Dimensional ◽  
Hopf Bifurcations ◽  
Bifurcation Parameter ◽  
Fast System ◽  
Stability Properties ◽  
Theoretical Results

AbstractA theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation parameter. With the aim of exemplifying and validating the theoretical results, numerical simulations are also undertaken, which reveal rich bursting behavior in the three-dimensional fractional-order slow-fast system.

scholarly journals Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhanying Yang ◽  
Jie Zhang ◽  
Junhao Hu ◽  
Jun Mei
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Finite Time ◽  
Analytical Techniques ◽  
Stability Criteria ◽  
Time Stability ◽  
Practical Applications ◽  
Finite Time Stability

This paper focuses on a class of delayed fractional Cohen–Grossberg neural networks with the fractional order between 1 and 2. Two kinds of criteria are developed to guarantee the finite-time stability of networks based on some analytical techniques. This method is different from those in some earlier works. Moreover, the obtained criteria are expressed as some algebraic inequalities independent of the Mittag–Leffler functions, and thus, the calculation is relatively simple in both theoretical analysis and practical applications. Finally, the feasibility and validity of obtained results are supported by the analysis of numerical simulations.

scholarly journals Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Chaotic Circuit ◽  
Control Scheme

In this paper, the anti-synchronization of fractional-order chaotic circuit with memristor (FCCM) is investigated via a periodic intermittent control scheme. Based on the principle of periodic intermittent control and the Lyapunov stability theory, a novel criterion is adopted to realize the anti-synchronization of FCCM. Finally, some examples of numerical simulations are exploited to verify the feasibility of theoretical analysis.

Analysis on Cellular Neural Networks with Negative Slope Activation Function

2013 ◽  
Vol 427-429 ◽  
pp. 2493-2496
Author(s):  
Qi Han ◽  
Qian Xiong ◽  
Chao Liu ◽  
Jun Peng ◽  
Le Peng Song ◽  
...  
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Activation Function ◽  
Cellular Neural Networks ◽  
Negative Slope ◽  
The Relationship ◽  
Inputs And Outputs

In the paper, the region of the number of equilibrium points of every cell in cellular neural networks with negative slope activation function is considered by the relationship between parameters of cellular neural networks. Some conditions are obtained by using the relationship among connection weights. Depending on these sufficient conditions, inputs and outputs of a CNN, the regions of the values of parameters can be obtained. Some numerical simulations are presented to support the effectiveness of the theoretical analysis.

scholarly journals Chaos Synchronization between Two Different Fractional Systems of Lorenz Family

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
A. E. Matouk
Keyword(s):  
Theoretical Analysis ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Order Parameter ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chen System ◽  
Fractional Systems ◽  
Lü System

This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenz-like system. The analytical conditions for the synchronization of these pairs of different fractional order chaotic systems are derived by utilizing Laplace transform. Numerical simulations are used to verify the theoretical analysis using different values of the fractional order parameter.

Synchronization and anti-synchronization of a fractional order delayed memristor-based chaotic system using active control

2018 ◽  
Vol 32 (14) ◽  
pp. 1850142 ◽  
Author(s):  
Dawei Ding ◽  
Xin Qian ◽  
Nian Wang ◽  
Dong Liang
Keyword(s):  
Time Delay ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Control Strategy ◽  
Active Control Strategy

In this paper, the issue of synchronization and anti-synchronization for fractional-delayed memristor-based chaotic system is studied by using active control strategy. Firstly, some explicit conditions are proposed to guarantee the synchronization and anti-synchronization of the proposed system. Secondly, the influence of order and time delay on the synchronization (anti-synchronization) is discussed. It reveals that synchronization (anti-synchronization) is faster as the order increases or the time delay decreases. Finally, some numerical simulations are presented to verify the validity of our theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document