arXiv subjects
Publications and source records attributed to Hidetsugu Sakaguchi.
We study a simple replicator model with non-symmetric and nonlocal interactions. Hierarchical structures with prey-predator relations are self-organized from a homogeneous state, induced by the dynamical instability of nonlinear interactions.
Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.
A one-dimensional model of a dispersive medium with intrinsic loss, compensated by a parametric drive, is proposed. It is a combination of the well-known parametrically driven nonlinear Schrödinger (NLS) and complex cubic Ginzburg-Landau equations, and has various physical applications (in particular, to optical systems). For the case when the zero background is stable, we elaborate an analytical approximation for solitary-pulse (SP) states. The analytical results are found to be in good agreement with numerical findings. Unlike the driven NLS equation, in the present model SPs feature a nontrivial phase structure. Combining the analytical and numerical methods, we identify a stability region for the SP solutions in the model's parameter space. Generally, the increase of the diffusion and nonlinear-loss parameters, which differ the present model from its driven-NLS counterpart, lead to shrinkage of the stability domain. At one border of the stability region, the SP is destabilized by the Hopf bifurcation, which converts it into a localized breather. Subsequent period doublings make internal vibrations of the breather chaotic. In the case when the zero background is unstable, hence SPs are irrelevant, we construct stationary periodic solutions, for which a very accurate analytical approximation is developed too. Stability of the periodic waves is tested by direct simulations.
We study dendritic growth numerically with a phase field model. Tip oscillation and regular side-branching are observed in a parameter region where the anisotropies of the surface tension and the kinetic effect compete. The transition from a needle pattern to a dendritic pattern is conjectured to be a supercritical Hopf bifurcation.
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.
We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a single block and spring system. However, we find that the transition is continuous in a long chain of blocks and springs. The size distribution of stick-slip motions exhibits a power law at the critical point.
Two models of driven optical cavities, based on two-dimensional Ginzburg-Landau equations, are introduced. The models include loss, the Kerr nonlinearity, diffraction in one transverse direction, and a combination of diffusion and dispersion in the other one (which is, actually, a temporal direction). Each model is driven either parametrically or directly by an external field. By means of direct simulations, stable completely localized pulses are found (in the directly driven model, they are built on top of a nonzero flat background). These solitary pulses correspond to spatio-temporal solitons in the optical cavities. Basic results are presented in a compact form as stability regions for the solitons in a full three-dimensional parameter space of either model. The stability region is bounded by two surfaces; beyond the left one, any two-dimensional (2D) pulse decays to zero, while quasi-1D pulses, representing spatial solitons in the optical cavity, are found beyond the right boundary. The spatial solitons are found to be stable both inside the stability region of the 2D pulses (hence, bistability takes place in this region) and beyond the right boundary of this region (although they are not stable everywhere). Unlike the spatial solitons, their quasi-1D counterparts in the form of purely temporal solitons are always subject to modulational instability, which splits them into an array of 2D pulses, that further coalesce into two final pulses. A uniform nonzero state in the parametrically driven model is also modulationally unstable, which leads to formation of many 2D pulses that subsequently merge into few ones.
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor. The diffusion constants are numerically calculated for convection models with free and rigid boundary conditions.
We study domain structures in bistable systems such as the Ginzburg-Landau equation. The size of domains can be controlled by a global negative feedback. The domain-size control is applied for a localized spiral pattern.
A system consisting of the cubic complex Ginzburg-Landau equation which is linearly coupled to an additional linear dissipative equation, is considered. The model was introduced earlier in the context of dual-core nonlinear optical fibers with one active and one passive cores. We argue that it may also possibly describe traveling-wave convection in a channel with an inner vertical partition. By means of systematic simulations, we find new types of stable localized excitations, which exist in the system in addition to the earlier found stationary pulses. The new localized excitations include pulses existing on top of a small-amplitude background (that may be regular or chaotic) {\em above} the threshold of instability of the zero solution, and breathers into which stationary pulses are transformed through a Hopf bifurcation below the zero-solution instability threshold. A sharp border between the stable stationary pulses and breathers, precluding their coexistence, is identified. Stable bound states of two breathers with a phase shift $π/2$ between their internal vibrations are found too. Above the threshold, the pulses are standing if the small-amplitude background oscillations are regular; if the background is chaotic, the pulses are randomly walking. With the increase of the system's size, more randomly walking pulses are spontaneously generated. The random walk of different pulses in a multi-pulse state is synchronized (but not completely) due to their mutual repulsion. At a large overcriticality, the multi-pulse state goes over into a spatiotemporal chaos.