Canards are characteristic phenomena of singularly perturbed systems with multiple time scales. Using the Bonhoeffer-van der Pol equations, we perform asymptotic analysis to obtain the parameter values where a canard solution exists. Although the system is two-dimensional, the numerical computations of the equations show a seemingly chaotic phenomenon at these parameter values. Consequently, high-precision numerical computations are employed to quantitatively evaluate both the convergent and divergent dynamics near a canard solution. The numerically produced fake chaos is attributed to insufficient precision of the stable dynamics.
Herding systems are discrete-time nonlinear dynamical systems designed efficiently for statistical inference. In this paper, we introduce a continuous-time version of these systems, which we call herding billiard systems. In contrast to the weakly chaotic dynamics of the original version, the continuous-time version is shown to have chaotic pseudo-billiard dynamics, while inheriting the fundamental sampling functions. We also present the connection between these two versions. Thus, herding billiard systems provide a novel approach to the complexity of herding systems from the viewpoint of chaotic billiard dynamics.
In this paper, we propose a novel control method for nonholonomic constrained systems using coupled oscillators composed through the Kuramoto model. The Kuramoto model is a mathematical model used to describe synchronization phenomenona. We focus on the Kuramoto model because it is able to generate stable rhythmic signals that are modulable for engineering, and because it is sufficiently simple for mathematical analysis. The contributions of this paper are twofold. First, we propose the use of a pair of Kuramoto oscillators as dynamic controllers for a nonholonomic Brockett integrator system;next, we define a feedback control scheme by adjusting its angular velocities based on the system state. We then derive stability criteria for the entire feedback system and examine the effectiveness of the system through several numerical simulations. We also show that the proposed idea is applicable to a two-wheeled vehicle system, which is locally equivalent to the Brockett integrator under proper coordinate and input transformations. Second, we apply the proposed method to control the walking distance of a quadrupedal quasi-passive dynamic walker and examine the effectiveness of the proposed method through walking experiments.
This paper presents a novel autonomous chaotic system defined by a second-order piecewise linear system on the cylinder-type phase space and hysteresis switching. This system can generate super-expanding chaos characterized by a very large positive Lyapunov exponent. Using the piecewise linear one-dimensional return map, the chaos generation is guaranteed theoretically. Presenting a simple test circuit, typical phenomena are confirmed experimentally.
Recently, the pseudo-transient analysis (PTA) methods have been researched as one of the most effective continuation methods to overcome the non-convergence problem of the Newton-Raphson method for finding the DC operating points of nonlinear circuits. However, the former PTA methods have a time-consuming problem, especially for some large-scale circuits. In this paper, we combine an effective ramping algorithm with two proposed ramping functions and the damped PTA (DPTA) algorithm together to improve the simulation efficiency. It can eliminate the oscillation and time-consuming problems at the same time. Besides, a restart method in the SPICE3 implementation is also proposed, which is effectively to improve convergence when the circuit is stuck in an infinite loop and fails to converge during the simulation. Numerical examples demonstrate the efficiency and convergence improvement of the proposed algorithms.
The purpose of this paper is to improve the output quality of three phase PWM DC-AC inverter. The improvement in output quality is required to reduce the harmonic components. The PWM control can reduce harmonic components by adjusting the width of each pulse. We design the switching phase to improve output quality, also propose an evaluation function for evaluating the frequency components. In order to optimize the switching phase, particle swarm optimization is applied. We confirm the effectiveness of the proposed method comparing with other methods. Moreover, we confirm the effectiveness by using the implementation circuit of the three phase inverter.
Stochastic resonance (SR) is a nonlinear phenomenon that, under certain conditions, can enhance system response by adding noise to the signals of some nonlinear system. A particular advantage of SR over conventional linear systems is that it is able to detect subthreshold signals that linear systems hardly sense. Unfortunately, most research of SR in wireless communication systems has focused on fundamental analysis, leaving work to be done in experimental SR research despite the attractiveness of its application. Few attempts have so far addressed the development of SR receivers to show the feasibility of subthreshold signal detection. Those receivers that have been developed are simple ones specially made to confirm the usefulness of SR without needing to support state-of-the-art wireless radio technology. The purpose of this study is to examine the feasibility of using an SR receiver to receive subthreshold radio frequency (RF) signals. A new add-on SR device is developed and confirmation that the SR phenomenon exists within RF is obtained when using software defined radio (SDR) as the post-processing receiver. Furthermore, bit error rate (BER) performance is mainly governed by the add-on SR device's output signal quality.
In the present paper, we investigate the description ability of digital sound data by the rule set of one dimensional cellular automata with two state and three neighbors referred to as 1-2-3 CA hereafter. It has been shown that the two-rules set of (#90, #180) has the highest description ability of all the possible two-rules sets. For several sound data, however, the data amount of the resultant codes becomes larger than original data, originating into the limitations of the two-rules set of (#90, #180). In order to overcome the limitations, we try to improve the description ability of digital sound data by adding another rule to (#90, #180). Therefore, we evaluate the description ability for the all the possible sets, where we add another rule to (#90, #180). From computer experiments, for the three-rules set of (#45, #90, #180), the averaged length of the rule sequences of the resultant codes becomes shorter, and a ratio of the reduced search number takes larger for all the data. Thus, we succeed to improve the description ability.
In the present paper, we investigate roles of the randomness of memory patterns in the sensitive response of the chaotic associative memory dynamics to memory pattern fragments in the chaotic neural network model referred to as CNN hereafter. In order to realize a memory search for hierarchical memory patterns, we overcome the problem how to construct the hierarchical memory patterns, whose basin volumes and visiting measures are sufficiently large. Therefore, we investigate (i) how to construct the memory patterns which gives sufficiently large basin volumes of theirs in a recurrent neural network model referred to as RNN hereafter, and (ii) the sensitivity of the chaotic associative memory dynamics in CNN to memory pattern fragments, focusing on the randomness in the memory patterns. From computer experiments, the basin volumes of the memory patterns become much larger as the randomness increases. In addition, the sensitive and robust response to the memory pattern fragments is achieved as the randomness becomes larger. Thus, ensuring sufficient large basin volumes and visiting measures with the same frequency, and the quite sensitive and robust response to the memory pattern fragments, the randomness in memory patterns is practical, which introduces the small overlap among each inter-cycle pattern.
Micro-texts emerging from social media platforms have become an important source for research. Automatized classification and interpretation of such micro-texts is challenging. The problem is exaggerated if the number of texts is at a medium level, making it too small for effective machine learning, but too big to be efficiently analyzed solely by humans. We present a semi-supervised learning system for micro-text classification that combines machine learning techniques with the unmatched human ability for making demanding, i.e. nonlinear decisions based on sparse data. We compare our system with human performance and a predefined optimal classifier using a validated benchmark data-set.
In order to develop large-scale nonlinear dynamical systems using CMOS integrated circuits, we propose a core circuit for coupled map lattice (CML) models. The characteristics of the core circuits in the lattice on a chip are not generally equal, which is caused by CMOS device mismatches, including parasitic capacitance and wiring resistance. The proposed circuit solves this problem; it compensates for a DC offset voltage variation by holding it at a capacitor, and also for current variation by adjusting the bias voltage of a current source automatically so as to bring the current close to a target value. The proposed core circuit has been designed and fabricated using TSMC 0.25 µm CMOS technology. The measurement results using the fabricated circuit have shown that the bit precision is more than 8 bits, even if there is a DC offset voltage of 100 mV or a bias-voltage change of 100 mV in a switched current source.