We propose a novel controlling methodology for avoiding local bifurcations of stable, hyperbolic fixed and periodic points in nonlinear discrete-time dynamical systems with parameter variation. Dynamical systems may not work as expected owing to bifurcations of desired behavior caused by parameter variation. Controlling parameters to avoid bifurcations enables us to construct robust dynamical systems against unexpected parameter variation. Assuming that desired behavior is a hyperbolic fixed or periodic point, as a control strategy, optimizing the degree of its stability (i.e. the maximum modulus of its characteristic multipliers) is considerable. However, it cannot be optimized by simple gradient methods, and off-line calculation to find the exact positions of fixed and periodic points and their characteristic multipliers is also needed. In contrast, the method we propose is to control the maximum local Lyapunov exponent (MLLE) that is defined in finite time and is closely related to the degree of stability on hyperbolic fixed and periodic points. This method can predict occurrence of local bifurcations for parameter variation by monitoring the MLLE along the passage of time and adjust parameter values on line to control the MLLE. This leads that occurrence of local bifurcations can be avoided without directly analyzing bifurcations in advance. The parameter regulation to avoid local bifurcations is theoretically derived from the minimization of an objective function with respect to the MLLE. Our experimental results applied to the Kawakami and Hénon maps demonstrate that the proposed controller could be used to avoid local bifurcations.
Public opinion is formed through social interactions of individuals. A mechanism behind the formation of a highly dominant public opinion is a sociological theory called the spiral of silence. Here we study opinion dynamics resulting from the spiral of silence, using an agent-based model with complex interaction networks. We show that an extremely dominant public opinion arises in the presence of a moderate proportion of neutrals and its dominance level is enhanced by social interactions. Furthermore, we demonstrate that a correlation between characteristics and social interactions of the individuals has a large influence on the opinion formation dynamics.
In this paper, we propose a clustered model reduction method for interconnected second-order systems evolving over undirected networks, which we call second-order networks. In this model reduction method, network clustering, i.e., clustering of subsystems, is performed according to cluster reducibility, which is defined as a notion of weak controllability of local subsystem states. This paper clarifies that the cluster reducibility can be algebraically characterized for second-order networks through the controller-Hessenberg transformation of their first-order representation. By aggregating the reducible clusters, we obtain an approximate model that preserves an interconnection topology among clustered subsystems. Furthermore, we derive an H∞-error bound of the state discrepancy caused by the cluster aggregation. Finally, the efficiency of the proposed method is demonstrated through an example of large-scale complex networks.
Many stochastic systems require multiple trials to estimate their time-varying statistics. Time-varying statistics are often estimated by employing a time window of a certain length over trials. However, no standardized method exists for estimating time-varying statistics. In this paper, we propose an analysis method for measuring time-varying statistics that can be applied to point process data with multiple trials, such as neural spike trains.
Mathematical models of HIV-1 infection including an eclipse phase are virologically reasonable and affect on quantifying viral dynamics of acute HIV-1 infection compared with models without the eclipse phase. However, it remains unclear how the modeling of the eclipse phase changes the estimated values of kinetic parameters and derived quantities, because, so far, most of studies quantifying viral dynamics are limited on analysing viral load datasets. Furthermore, the data analysis is essentially based on piece wise linear regression of the log transformed viral loads. Using the time course data of target cell densities and viral load from HIV-1 infected humanized mouse, we herein derived a novel delay differential equation model and investigated the effect of the eclipse phase on quantifying acute viral dynamics. Our findings suggest that modeling of the eclipse phase affects especially on the infection rate of viruses and the death rate of infected cells but not on the initial viral growth rate in HIV-1 infected humanized mouse.
Immunotherapy for cancer is a forthcoming therapeutic option in cancer treatment. A variety of approaches, including adoptive cell transfer, adjuvant therapy, and monoclonal antibody therapy, are currently used as complementary or alternative cancer treatments. Since immunity against tumors is established as a result of complex interactions among tumors and immune cells, a theoretical framework to elucidate the dynamics of tumor killing by immune cells initiated by clinical intervention needs to be developed. We construct a simple mathematical model that describes the killing of tumors by T cells. We focus on a mathematical characterization of the effect of adoptive cell transfer therapy, the injection of a patient's own ex vivo activated T cells to initiate tumor immunity. On the basis of rigorous mathematical analyses and numerical computations, we provide biological interpretations for the possible outcomes of adoptive cell transfer under three different scenarios in terms of proliferation. In our modeling framework, adoptive cell transfer therapy can be understood as a driving force that potentially operates to shift the state of an immune response from inactive to active. On the other hand, our modeling framework suggests the possibility that a tumor can exploit a self-augmenting proliferation of T cells mediated by autocrine/paracrine signaling as an escape strategy from an immune response.
A salient feature of complex systems is their inherent robustness against poor and fluctuating characteristics of constituent elements, systematic offsets in parameter values, environmental changes, noise, and other such fluctuations. In spite of such unreliable, poor-quality, and highly variable elements, complex systems generally exhibit high-quality behavior as a whole. In this paper, we exploit this inherent robustness of complex systems to create a compact and efficient realization of a hardware system for exponential chaotic tabu search. We start from a synchronous exponential chaotic tabu search algorithm and develop a novel partial-update exponential chaotic tabu search algorithm. The proposed algorithm is suitable for a large-scale analog/digital hybrid hardware implementation. In addition, a hardware system architecture suitable for the partial-update exponential chaotic tabu search is proposed, and a switched-current chaotic neuron integrated circuit dedicated to the proposed system architecture is also designed. We investigate the feasibility of implementing the digital part of the system with a field-programmable gate array.
This paper proposes a pulse-coupled system with three spiking neurons. The neurons operate integrate-and-fire dynamics and output a spike. When this happens, another neuron accepts the spiked output and is compelled to fire: In this way, a ring of three neurons are coupled. As the parameter is varied, the behavior becomes a master-slave conjunction. We clarify the theoretical results for various boundary conditions and present the results of numerical simulations. Using a test circuit, we confirm the typical behavior of a pulse-coupled system.
A β-encoder, a non-binary analog-to-digital converter that is based on the β-expansion, is reported to be robust to large process variations and widespread environment fluctuations. However, the quantization error of the β-encoder is complicatedly distributed and hard to be estimated due to the chaotic nature of the β-transformation. In this work, we propose an analysis method for determining an upper bound of the mean squared error of the quantization. We also provide an evaluation of the signal-to-quantization-noise ratio, which is useful for designing β-encoders.
A novel optimization method called, “optimizer using swarm of chaotic dynamical particles,” (OSCDP) is proposed. The proposed method searches for an optimal solution on the basis of particles governed by chaotic dynamics. The chaotic dynamics make the particles behave in a complex way, by stretching and holding mechanisms, even though the dynamics do not contain any stochastic terms. The particles share information of their best position that is a candidate of the optimal solution, as with particle swarm optimization (PSO). The complex behavior and the sharing information mechanism enable the proposed method to search for the optimal solution. This method consists of only three system parameters, making it suitable for implementing the algorithm. We compared the proposed method with other deterministic PSOs and the standard PSO, and found that the proposed method exhibited a better searching performance.