arXiv subjects

Kunihiko Kaneko

Publications and source records attributed to Kunihiko Kaneko.

At least 163 records · Page 9Linked to original sources

arXiv2001

Spontaneous structure formation in a network of chaotic units with variable connection strengths

As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural order emerges even without any inter-unit synchronization of dynamics. Within this structure, units spontaneously separate into two groups whose distinguishing feature is that the first group possesses many outwardly-directed connections to the second group, while the second group possesses only few outwardly-directed connections to the first. The relevance of the results to structure formation in neural networks is briefly discussed.

cond-mat.dis-nn↗

arXiv2001

How Fast Elements can Affect Slow Dynamics

A chain of coupled chaotic elements with different time scales is studied. In contrast with the adiabatic approximation, we find correlations between faster and slower elements when the differences in the time scales of the elements lie within a certain range. For such correlations to occur, three features are essential: strong correlations among the elements allowing for both synchronization and desynchronization, bifurcation in the dynamics of the fastest element by the change of its control parameter, and the cascade propagation of the bifurcation. The relevance of our results to biological memory is briefly discussed.

nlin.CD↗

arXiv2001

Origin of genetic information from minority control in a replicating system with mutually catalytic molecules

As the first step in an investigation of the origin of genetic information, we study how some species of molecules are preserved over cell generations and play an important role in controlling the growth of a cell. We consider a model consisting of protocells. Each protocell contains two mutually catalyzing molecule species ($X$ and $Y$), each of which has catalytically active and inactive types. One of the species $Y$ is assumed to have a slower synthesis speed. Through divisions of the protocells, the system reaches and remains in a state in which there are only a few active $Y$ and almost no inactive $Y$ molecules in most protocells, through selection of very rare fluctuations. In this state, the active $Y$ molecules are shown to control the behavior of the protocell. The minority molecule species act as the information carrier, due to the relatively discrete nature of its population, in comparison with the majority species which behaves statistically in accordance with the law of large numbers. The relevance of this minority controlled state to evolvability is discussed.

nlin.AO↗

arXiv2001

Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals

The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiation from `m ultipotent spots'. These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and as a result, an inhomogeneous pattern of spots is formed. This differentiation process of spots is analyzed in terms of the loss of chemical diversity and decrease of the local Kolmogorov-Sinai entropy. The relevance of the results to developmental cell biology and stem cells is also discussed.

nlin.PS↗

arXiv2000

Sympatric speciation: compliance with phenotype diversification from a single genotype

A novel mechanism for sympatric speciation that takes into account complex bio-processes within each individual organism is proposed. According to dynamical systems theory, organisms with identical genotypes can possess differentiated physiological states and may coexist `symbiotically' through appropriate mutual interaction. With mutations, the phenotypically differentiated organisms gradually come to possess distinct genotypes, while maintaining their symbiotic relationship. This symbiotic speciation is robust against sexual recombination, because offspring of mixed parentage, with intermediate genotypes, are less fit than their parents. This leads to sterility of the hybrid. Accordingly, a basis for mating preference also arises.

cond-mat↗

arXiv2000

Theory of Robustness of Irreversible Differentiation in a Stem Cell System: Chaos hypothesis

Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell systems - stochastic differentiation of stem cells and the robustness of a system due to regulation of this differentiation - are found to be general properties of a system of interacting cells exhibiting chaotic intra-cellular reaction dynamics and cell division, whose presence does not depend on the detail of the model. It is found that stem cells differentiate into other cell types stochastically due to a dynamical instability caused by cell-cell interactions, in a manner described by the Isologous Diversification theory. This developmental process is shown to be stable not only with respect to molecular fluctuations but also with respect to removal of cells. With this developmental process, the irreversible loss of multipotency accompanying the change from a stem cell to a differentiated cell is shown to be characterized by a decrease in the chemical diversity in the cell and of the complexity of the cellular dynamics. The relationship between the division speed and this loss of multipotency is also discussed. Using our model, some predictions that can be tested experimentally are made for a stem cell system.

nlin.AO↗

arXiv2000

Origin of complexity in multicellular organisms

Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems can exhibit complex pattern formation with spontaneous cell differentiation. Such systems employ a `cooperative' use of resources and maintain a larger growth speed than simple cell systems, which exist in a homogeneous state and behave 'selfishly'. The relevance of the diversity of chemicals and reaction dynamics to the growth of a multicellular organism is demonstrated. Chaotic biochemical dynamics are found to provide the multi-potency of stem cells.

nlin.AO↗

arXiv2000

Long-term Relaxation of a Composite System in Partial Contact with a Heat Bath

We study relaxational behavior from a highly excited state for a composite system in partial contact with a heat bath, motivated by an experimental report of long-term energy storage in protein molecules. The system consists of two coupled elements: The first element is in direct contact with a heat bath, while the second element interacts only with the first element. Due to this indirect contact with the heat bath, energy injected into the second element dissipates very slowly, according to a power law, whereas that injected into the first one exhibits exponential dissipation. The relaxation equation describing this dissipation is obtained analytically for both the underdamped and overdamped limits. Numerical confirmation is given for both cases.

cond-mat.stat-mech↗

arXiv2000

Energy Storage in a Hamiltonian System in Partial Contact with a Heat Bath

To understand the mechanism allowing for the long-term storage of excess energy in proteins, we study a Hamiltonian system consisting of several coupled pendula in partial contact with a heat bath. It is found that energy storage is possible when the motion of each pendulum switches between oscillatory (vibrational) and rotational (phase-slip) modes. The storage time increases almost exponentially to the square root of the injected energy. The relevance of our mechanism to protein motors is discussed.

cond-mat.stat-mech↗

arXiv1999

Robust and Irreversible Development in Cell Society as a General Consequence of Intra-Inter Dynamics

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. "Stem cells" that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.

chao-dyn↗

arXiv1999

Sensitive boundary condition dependence of noise-sustained structure

Sensitive boundary condition dependence (BCD) is reported in a convectively unstable system with noise, where the amplitude of generated oscillatory dynamics in the downstream depends sensitively on the boundary value. This BCD is explained in terms of the manner in which the co-moving Lyapunov exponent (characterizing the convective instability) decreases from upstream to downstream. It is shown that a fractal BCD appears if the dynamics that represent the spatial change of the fixed point includes transient chaotic dynamics. By considering as an example a one-way-coupled map lattice, this theory for BCD is demonstrated.

chao-dyn↗

arXiv1999

Energy Absorption and Storage in a Hamiltonian System in Partial Contact with a Heat Bath

To understand the mechanism allowing for long-term storage of excess energy in proteins, we study a Hamiltonian system consisting of several coupled pendula in partial contact with a heat bath. It is found that energy absorption and storage are possible when the motion of each pendulum switches between oscillatory (vibrational) and rotational modes. The relevance of our mechanism to protein motors is discussed.

chao-dyn↗

arXiv1998

Noiseless Collective Motion out of Noisy Chaos

We consider the effect of microscopic external noise on the collective motion of a globally coupled map in fully desynchronized states. Without the external noise a macroscopic variable shows high-dimensional chaos distinguishable from random motion. With the increase of external noise intensity, the collective motion is successively simplified. The number of effective degrees of freedom in the collective motion is found to decrease as $-\log{σ^2}$ with the external noise variance $σ^2$. It is shown how the microscopic noise can suppress the number of degrees of freedom at a macroscopic level.

chao-dyn↗

arXiv1998

Life as Complex Systems --- Viewpoint from Intra-Inter Dynamics

Basic problems in complex systems are surveyed in connection with Life. As a key issue for complex systems, complementarity between syntax/rule/parts and semantics/behavior/whole is stressed. To address the issue, a constructive approach for a biological system is proposed. As a construction in a computer, intra-inter dynamics is presented for cell biology, where the following five general features are drawn from our model experiments; intrinsic diversification, recursive type formation, rule generation, formation of internal representation, and macroscopic robustness. Significance of the constructed logic to the biology of existing organisms is also discussed.

adap-org↗

arXiv1998

Noise-induced Input Dependence in a Convective Unstable Dynamical System

Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow dynamics, shows both analogue and digital changes, where the former is represented by oscillation frequency and the latter by different type of dynamics. The underlying universal mechanism for these changes is clarified by the spatial change of the co-moving Lyapunov exponent, with which the condition for the input dependence is formulated. The mechanism has a remarkable dependence on the noise strength, and works only within its medium range. Relevance of our mechanism to intra-cellular signal dynamics is discussed, by making our dynamics correspond to the auto-catalytic biochemical reaction for the chemical concentration, and the input to the external signal, and the noise to the concentration fluctuation of chemicals.

chao-dyn↗

arXiv1998

Collective Chaos

An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of low-dimensional collective chaos is confirmed, where the scale of (high-dimensional) microscopic chaos is separated from the macroscopic motion, and the scale approaches zero in the thermodynamic limit. pacs:05.45+b,05.90+m,64.60.Cn

chao-dyn↗

arXiv1998

On the Tongue-Like Bifurcation Structures of the Mean-Field Dynamics in a Network of Chaotic Elements

Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the tongue-like structure of collective motions in parameter space. Such collective motion is supported by the separation of time scale, given by the self-consistent relationship between the collective motion and chaotic dynamics of each element. It is shown that the change of collective motion is related with the window structure of a single one-dimensional map. Formation and collapse of regular collective motion are understood as the internal bifurcation structure. Coexistence of multiple attractors with different collective behaviors is also found in fully desynchronized state. 05.45+b,05.90+m,87.10+e Keywords: Globally coupled map, Mean field dynamics, Collective motion

chao-dyn↗

arXiv1998

On the Strength of Attractors in a High-dimensional System: Milnor Attractor Network, Robust Global Attraction, and Noise-induced Selection

Strength of attractor is studied by the return rate to itself after perturbations, for a multi-attractor state of a globally coupled map. It is found that fragile (Milnor) attractors have a large basin volume at the partially ordered phase. Such dominance of fragile attractors is understood by robustness of global attraction in the phase space. Change of the attractor strength and basin volume against the parameter and size are studied. In the partially ordered phase, the dynamics is often described as Milnor attractor network, which leads to a new interpretation of chaotic itinerancy. Noise-induced selection of fragile attractors is found that has a sharp dependence on the noise amplitude. Relevance of the observed results to neural dynamics and cell differentiation is also discussed.

chao-dyn↗