Woo-Sik Son

Chaotic universe in the z=2 Horava-Lifshitz gravity

The deformed

Time Delay Effect on the Love Dynamical Model

z=2

Mixmaster universe in the z = 3 deformed Hořava-Lifshitz gravity

Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity with coupling constant

Exceptional points in coupled dissipative dynamical systems.

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Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling

leads to a nonrelativistic mixmaster cosmological model. The potential of theory is given by the sum of IR and UV potentials in the ADM Hamiltonian formalism. It turns out that adding the UV potential cannot suppress chaotic behaviors existing in the IR potential.

Chaotic universe in thez=2Hořava-Lifshitz gravity

We investigate the effect of time delay on the dynamical model of love. The local stability analysis proves that the time delay on the return function can cause a Hopf bifurcation and a cyclic love dynamics. The condition for the occurrence of the Hopf bifurcation is also clarified. Through a numerical bifurcation analysis, we confirm the theoretical predictions on the Hopf bifurcation and obtain a universal bifurcation structure consisting of a supercritical Hopf bifurcation and a cascade of period-doubling bifurcations, i.e., a period doubling route to chaos.

A non-chaotic mixmaster universe in the z=2 Hovava-Lifshitz gravity

The z = 3 deformed Hořava-Lifshitz gravity with coupling constants ω and ϵ leads to a nonrelativistic “mixmaster” cosmological model. The potential of theory is given by the sum of IR and UV potentials in the ADM Hamiltonian formalism. It turns out that the presence of the UV-potential cannot suppress chaotic behaviors existing in the IR-potential, which comes from curvature anisotropy.

Delayed feedback on the dynamical model of a financial system

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

Current reversal with type-I intermittency in deterministic inertia ratchets.

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Transport control in a deterministic ratchet system

The deformed