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Chil-Min Kim

Publications and source records attributed to Chil-Min Kim.

27 records · Page 2Linked to original sources
arXiv2004

Synchronization of Chaotic Oscillators due to Common Delay Time Modulation

We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common^M chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by^M a signal of another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov exponents and discuss it in relation with generalized synchronization.^M

nlin.CD↗
arXiv2004

Origin of the Transition Inside the Desynchronized State in Coupled Chaotic Oscillators

We investigate the origin of the transition inside the desynchronization state via phase jumps in coupled chaotic oscillators. We claim that the transition is governed by type-I intermittency in the presence of noise whose characteristic relation is $ \propto \exp(α|ε_t -ε|^{3/2})$ for $ε_t -ε<0$ and $ \propto (ε_t -ε)^{-1/2}$ for $ε_t -ε>0$, where $ $ is the average length of the phase locking state and $ε$ is the coupling strength. To justify our claim we obtain analytically the tangent point, the bifurcation point, and the return map which agree well with those of the numerical simulations.

nlin.CD↗
arXiv2004

Generalized Phase Synchronization in unidirectionally coupled chaotic oscillators

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are driven by correlated (but not identical) inputs from the drive oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and clarify its characteristics using Lyapunov exponents and phase difference plots.

nlin.CD↗
arXiv2004

Characteristics of a Delayed System with Time-dependent Delay Time

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications.

nlin.CD↗
arXiv2001

Phase Synchronization with Type-II Intermittency in Chaotic Oscillators

We study the phase synchronization (PS) with type-II intermittency showing $\pm 2 π$ irregular phase jumping behavior before the PS transition occurs in a system of two coupled hyperchaotic Rössler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has $2 π$-periodic minima. We characterize it as type-II intermittency with external noise through the return map analysis. In $ε_{t} < ε< ε_{c}$ (where $ε_{t}$ is the bifurcation point of type-II intermittency and $ε_{c}$ is the PS transition point in coupling strength parameter space), the average length of the time interval between two successive jumps follows $ \sim \exp(\midε_{t} - ε\mid^{2})$, which agrees well with the scaling law obtained from the Fokker-Planck equation.

chao-dyn↗
arXiv2001

Mechanism of synchronization in a random dynamical system

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, \emph{a modified definition} of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.

nlin.CD↗
arXiv1999

Characteristic Relations of Type-I Intermittency in the Presence of Noise

Near the point of tangent bifurcation, the scaling properties of the laminar length of type-I intermittency are investigated in the presence of noise. Based on analytic and numerical studies, we show that the scaling relation of the laminar length is dramatically deformed from $\frac{1}{\sqrtε}$ for $ε>0$ to $\exp\{\frac{1}{D}|ε|^{3/2}\}$ for $ε<0$ as $ε$ passes the bifurcation point $(ε=0)$. The results explain why two coupled Rössler oscillators exhibit deformation of the scaling relation of the synchronous length in the nearly synchronous regime.

chao-dyn↗
arXiv1998

Characteristic Relations of Type-III Intermittency in an Electronic Circuit

It is reported that the characteristic relations of type-II and type-III intermittencies, with respective local Poincar$\acute{e}$ maps of $x_{n+1}= (1+ε)x_n + a x^3_n$ and $x_{n+1}= - (1+ε)x_n - a x^3_n$, are both $- ln (ε)$ under the assumption of uniform reinjection probability. However, the intermittencies have various characteristic relations such as $ε^{-ν}$ ($1/2 \leq ν\leq 1$) depending on the reinjection probability. In this Letters the various characteristic relations are discussed, and the $ε^{-1/2}$ characteristic relation is obtained experimentally in an electronic circuit, with uniform reinjection probability.

chao-dyn↗