1 / 6

Characterization of The Noise Effect on The Weak Synchronization

 : A uniform random variable with and a unit variance. Characterization of The Noise Effect on The Weak Synchronization. W. Lim 1 , S.-Y. Kim 1 , and A. Jalnine 2 1 Department of Physics, Kangwon National University 2 Department of Nonlinear Processes

cleary
Download Presentation

Characterization of The Noise Effect on The Weak Synchronization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. : A uniform random variable with and a unit variance Characterization of The Noise Effect on The Weak Synchronization W. Lim1, S.-Y. Kim1, and A. Jalnine2 1Department of Physics, Kangwon National University 2Department of Nonlinear Processes Saratov State University, Russia  Unidirectionally Coupled 1D Maps  : Noise Strength  Effects of The Noise (a=1.82 and =0.0005) Weak Synchronization Weak Synchronization Strong synchronization c ct,l, Riddling Transition cb,r, Blow-out Bif. cb,l, Blow-out Bif. ct,r, Bubbling Transition c = -2.91 c = -0.7 c = -1.5

  2. Characterization of The Noise Sensitivity of The SCA Successive Transverse Bifurcations of The Periodic Saddles Embedded in The SCA  Local Transverse Repulsion of The Transverse Unstable Periodic Orbits  A typical trajectory may have segments exhibiting positive local Lyapunov exponents.  The weakly stable SCA becomes sensitive with respect to the variation of the noise intensity. Characterization of The Noise Sensitivity by the derivative of the un (=xn-yn). Noise Sensitivity Function Intermittent behavior of |SN| c = -0.7 c = -0.7

  3. Characterization of The Noise Effects  Noise Sensitivity Exponent(NSE)  Noise Sensitivity Function The minimum value of N with respect to the randomly chosen initial orbit points on the diagonal  Characterization of The Noise Sensitivity NSEs(circles) become the same as Parameter Sensitivity Exponents(PSEs: crosses). c = -0.7,  = 2.58

  4. Parameter and Noise Sensitivity Noise Sensitivity: Parameter Sensitivity: Since the values of  and fa are bounded, the boundedness of the is determined by the RM  NSEs become the same as PSEs. Probability distribution function for  Probability distribution function for fa

  5. Characterization of The Bubbling Attractor and Chaotic Transient  Laminar Phase Exponent  Average Laminar Length (Take the trajectory starting from (0,0) until 50,000 laminar phase are obtained.)  Characterization of The Bubbling Attractor =1/ (Reciprocal values of : crosses)  Chaotic Transient Exponent  Average Lifetime (Take the 1,000 randomly chosen initial conditions on the diagonal.)  Characterization of The Chaotic Transient =1/ (Reciprocal values of : crosses)

  6. Summary • Successive transverse bifurcations of the periodic saddles embedded in the SCA •  Local transverse repulsion of the transverse unstable periodic orbits •  A typical trajectory may have segments exhibiting positive local Lyapunov exponents. •  The weakly stable SCA becomes sensitive with respect to the variation of the • noise strength. • Quantitative Characterization of The Weak Synchronization by The Noise Sensitivity Exponents (NSEs)  For the case of bounded uniform noise, NSEs become the same as PSE characterizing the parameter sensitivity of the weakly stable SCA. • Characterization of The Bubbling Attractor and Chaotic Transient by The Laminar Phase Exponent  and The Chaotic Transient Exponent   and  have a reciprocal relation (1/).

More Related