FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

Learning to swim: a dynamical systems approach to mimicking fish swimming with CPG

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 361-369 ◽  
Author(s):  
Tianmiao Wang ◽  
Yonghui Hu ◽  
Jianhong Liang
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Systems Approach ◽  
Body Wave ◽  
Central Pattern Generators ◽  
Space Representation ◽  
Coupling Scheme ◽  
Locomotor Pattern ◽  
Learning Rules ◽  
A Chain

SUMMARYCentral Pattern Generators (CPGs) can generate robust, smooth and coordinated oscillatory signals for locomotion control of robots with multiple degrees of freedom, but the tuning of CPG parameters for a desired locomotor pattern constitutes a tremendously difficult task. This paper addresses this problem for the generation of fish-like swimming gaits with an adaptive CPG network on a multi-joint robotic fish. Our approach converts the related CPG parameters into dynamical systems that evolve as part of the CPG network dynamics. To reproduce the bodily motion of swimming fish, we use the joint angles calculated with the trajectory approximation method as teaching signals for the CPG network, which are modeled as a chain of coupled Hopf oscillators. A novel coupling scheme is proposed to eliminate the influence of afferent signals on the amplitude of the oscillator. The learning rules of intrinsic frequency, coupling weight and amplitude are formulated with phase space representation of the oscillators. The frequency, amplitudes and phase relations of the teaching signals can be encoded by the CPG network with adaptation mechanisms. Since the Hopf oscillator exhibits limit cycle behavior, the learned locomotor pattern is stable against perturbations. Moreover, due to nonlinear characteristics of the CPG model, modification of the target travelling body wave can be carried out in a smooth way. Numerical experiments are conducted to validate the effectiveness of the proposed learning rules.

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

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