Sun-Ho Choi

The dynamic behavior of Lohe oscillators on the unit sphere is examined under attractive and repulsive couplings. We introduce an order parameter measuring the degree of synchronization, which is defined by the modulus of a centroid of positions, and study the dynamics of this parameter. It is found that this order parameter completely characterizes equilibria up to constant motion for identical oscillators. Considering these identical oscillators, we show that the order parameter evolves from n

We present a Cucker-Smale-type flocking model for interacting multi-agents(or particles) moving with constant speed in arbitrary dimensions, and derive a sufficient condition for the asymptotic flocking in terms of spatial and velocity diameters, coupling strength and a communication weight. In literature, several Vicsek-type models with a unit speed constraint have been proposed in the modeling of self-organization and planar models were extensively studied via the dynamics of the heading angle

We present a quantum synchronization estimate of the Schrödinger–Lohe (S–L) model introduced by Lohe (2010 J. Phys. A: Math. Theor. 43 465301). The S–L model describes the dynamics of quantum oscillators on the nodes of a quantum network. When the coupling strength is positive and the maximal L2 distances between normalized initial wave functions are smaller than , we show that the L2 distances between wave functions converge to zero exponentially fast. Our result generalizes earlier work by Chi

We present a practical synchronization method for the Schrödinger–Lohe (S–L) system distinct potentials. The S–L model describes the spatial-temporal evolution of the wave functions of quantum Lohe oscillators on a network with Lohe couplings. When the potential effects are ignored, complete wave function synchronization (CWFS) can emerge in the sense that the L 2 -distance between wave functions exponentially approaches zero for a class of initial wave functions. In contrast, when the Lohe osci

We study time-delay effects on the synchronous dynamics of identical Lohe oscillators on the unit sphere. Time delays in the interactions between Lohe oscillators are induced by the finite propagation speed of information or communication, and generate some oscillatory phenomena in the initial time-layer near the initial time. From the viewpoint of synchronization, we provide a sufficient framework for the complete positional synchronization of Lohe oscillators in terms of their initial configur

We study the emergence of the mono-cluster flocking due to the interplay between the unit-speed constraint and time-delayed interactions in the evolution of the Cucker-Smale ensemble. Several flocking models with unit-speed constraint have been extensively used in the flocking modeling of self-propelled multi-agent systems in the control theory community. Time-delayed interactions can be caused by the finite propagation speed constraint in communications. In the previous literature, these two ph

We study the asymptotic behavior of an ensemble of identical Lohe oscillators on the unit sphere in the presence of small time delay interaction effects. When there is no time delay, the ensemble of identical Lohe oscillators collapses asymptotically to a one-cluster ensemble on the sphere; its asymptotic dynamics are governed by linear motion on the unit sphere with a constant natural velocity. We show that the presence of a small time delay can induce rich dynamical features such as asymptotic

We study the asymptotic behavior of dispersing solutions to the Vlasov-Poisson system. Due to long interaction range, we do not expect linear scattering (Choi S-H and Ha S-Y 2011 SIAM J. Math. Anal. 43 2050-77). Instead, we prove a modified scattering result (or long range scattering result) of small and dispersing solutions. We find a quasi-free forward trajectory so that along the trajectory, the solution has an asymptotic limit. We extract the logarithmic growth part of the Duhamel term, and

We propose a multi-stage structured rumor spreading model that consists of ignorant, new spreader, old spreader, and stifler.We derive a mean field equation to obtain the multi-stage structured model on homogeneous networks. Since rumors spread from a few people, we consider a large population by setting the number of initial spread to one in total population $ n $ and limiting $ n $ to $ \infty $. We investigate a threshold phenomenon of rumor outbreak in the sense of the large population limit

The meaningful distance to biological organisms is not necessarily one measured by the Euclidean metric but possibly one by a metric that counts the amount of resources such as food. It is assumed in this paper that the distance for biological organisms is measured by the amount of food between two places. A new chemotaxis model is introduced as an application of this “metric of food.” It is shown that, if the walk length of a random walk system is given by such a metric, the well-known chemotac

We present a critical threshold phenomenon on the $L^1$-asymptotic completeness for the nonlinear Vlasov equation with a self-consistent force. For a long-ranged self-consistent force, we show that the nonlinear Vlasov equation has no $L^1$-asymptotic completeness, which means that the nonlinear Vlasov flow cannot be approximated by the corresponding free flow in $L^1$-norm time-asymptotically. In contrast, for a short-ranged force, the nonlinear Vlasov flow can be approximated by the free flow

We present a Cucker–Smale type flocking model on a sphere including three terms: a centripetal force, multi-agent interactions on a sphere, and inter-particle bonding forces. We consider a rotation operator to compare velocity vectors on different tangent spaces. Due to the geometric restriction, the rotation operator is singular at antipodal points and the relative velocity between two agents located at these points is not well-defined. We assume that the communication rate between two antipoda