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Anomalous Hopf Bifurcations in Symmetrically-coupled Period-doubling Systems
임우창,김상윤 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.56 No.3
We consider two symmetrically-coupled logistic maps, and investigate the effect of symmetry on Hopf bifurcations, giving rise to the birth of the daughter orbits encircling the symmetric anti-phase mother orbit (with a time shift of half a period). When the rotation numbers º of daughter orbits are rational (i.e., v = r/s; r and s: coprimes), anomalous Hopf bifurcations are found to occur due to the symmetry of the coupled system. For even r, a symmetric periodic attractor is born through a standard Hopf bifurcation while for odd r, a conjugate pair of asymmetric periodic attractors appears via a nonstandard double Hopf bifurcation. These symmetry-conserving and -breaking Hopf bifurcations are explained by using the concept of a half-cycle map of a symmetrically-coupled map. These anomalous Hopf bifurcations might be observed in real experiments of symmetrically-coupled period-doubling systems.
Strange Nonchaotic Bursting in a Quasiperiodically-forced Hindmarsh-Rose Neuron
임우창,김상윤 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.57 No.6
We study the transition from a silent state to a bursting state by varying the dc stimulus in the Hindmarsh-Rose neuron under quasiperiodic stimulation. For this quasiperiodically-forced case, a new type of strange nonchaotic (SN) bursting state is found to occur between the silent state and the chaotic bursting state. This is in contrast to the periodically-forced case where the silent state transforms directly to a chaotic bursting state. Using a rational approximation to the quasiperiodic forcing, we investigate the mechanism for the appearance of such an SN bursting state. Thus, a smooth torus (corresponding to a silent state) is found to transform to an SN bursting attractor through a phase-dependent subcritical period-doubling bifurcation. These SN bursting states, together with chaotic bursting states, are characterized in terms of the interburst interval, the bursting length, and the number of spikes in each burst. Both bursting states are found to be aperiodic complex ones. Consequently, aperiodic complex burstings may result from two dynamically different states with strange geometry (one is chaotic and the other is nonchaotic). Thus, in addition to chaotic burstings, SN burstings may become a dynamical origin for the complex physiological rhythms that are ubiquitous in organisms.
임우창 大邱敎育大學校 科學敎育硏究所 2023 과학·수학교육연구 Vol.46 No.-
상대성 이론이나 양자역학과 같은 고급 물리학은 초등과학교육 과정에서 다루지 않는다. 그러나, 영화나 쉽게 과학을 설명한 도서 등 다양한 매체를 통해 초등학생들이 고급 물리학의 자세한 원리와 내용은 몰라도, 그로 인해 발생하는 현상과 결과의 일부분 등은 편협적으로 나마 알고 있는 경우가 많다. 이에 대비하여 예비 초등교사를 대상으로 양자역학의 내용을 간단하게 설명한 경우에 그것이 과학적 상상력에 어떠한 영향을 미치는지를 확인해 보려고 하였다. 미래를 예측해 보는 실험 결과 양자 역학에 대한 강의를 미리 선행한 실험군이 대조군보다는 다양한 예측을 하지 못하는 경향이 있으며, 긍정적으로 미래를 예측하는 경향이 강하다.
Characterization of Weak Collective Neural Coherence
임우창,김상윤 한국물리학회 2010 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.57 No.5
We consider a large population of N globally coupled inhibitory subthreshold neurons (which cannot fire spontaneously without noise). In a range of noise intensity, an oscillating ensembleaveraged collective potential with small amplitude emerges via cooperation of the complex potentials of individual neurons. To characterize this “weak” collective neural coherence, we introduce a new coherence measure, M(CI c , based on the ensemble average of cross-correlations between the collective potential and the individual potentials. This newly-introduced measure M(CI) c can be regarded as a “statistical-mechanical” measure because it quantifies the average contribution of (microscopic) individual potentials to the (macroscopic) collective potential. As a result of regular oscillations of the collective-individual cross-correlation functions, M(CI) c may be used to detect weak collective coherence much better than the conventional “microscopic” measure, M(Ⅱ) c , based on the cross-correlations between individual potentials. Furthermore, the computation load for M(CI) c (∼N) is much reduced as compared to that for M(Ⅱ) c (∼N2).