Kunihiko Mitsubori

Dependent switched capacitor chaos generator and its synchronization

This paper discusses a circuit family including a dependent switched capacitor (DSC). The DSC function is instantaneously short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically. We also consider a master-slave system. If there does not exist a homoclinic orbit in the master chaos attractor, it exhibits either in-phase or inverse-phase synchronization of chaos. If there exists a homoclinic orbit, the synchronization is broken down. We explain the synchronization mechanism and evaluate its robustness theoretically. The theoretical results have been verified in laboratory experiments.

Control of chaos from a piecewise linear hysteresis circuit

This paper proposes a simple control method of chaos from a piecewise linear hysteresis circuit. We can derive one dimensional return map rigorously from the circuit. It enables us to prove chaos generation and to calculate the initial value for the desired unstable periodic orbit (UPO). The control method uses occasional proportional feedback in each linear region and must stabilize the desired UPO in a theoretical sense. The robustness of the control method is verified by laboratory experiment. >

A four-dimensional plus hysteresis chaos generator

This paper discusses a four-dimensional plus hysteresis autonomous chaotic circuit. The circuit dynamics are described by two symmetric four-dimensional linear equations connected to each other by hysteresis switchings. We transform the equation into Jordan form and derive theoretical formulas of its three-dimensional return map, its Jacobian matrix and its Jacobian. These formulas can be developed easily to general dimensional cases and are used to evaluate Lyapunov exponents. Also we have discovered a torus doubling route to chaos and then to hyperchaos. Some of the return map attractors are confirmed by laboratory experiments. A rough two parameters bifurcation diagram is also given. >

Mutually pulse-coupled chaotic circuits by using dependent switched capacitors

This paper considers a mutually pulse-coupled system of chaotic circuits. Each circuit has a switch to short its capacitor, and the mutually pulse-coupling is realized by impulsive and simultaneous switching of the capacitors, depending on the states of both circuits. The coupled system exhibits synchronization of chaos and breakdown. The error expanding ratio between the units can be described by a simple theoretical formula. It enables us to classify the phenomena and to evaluate the dependence of the error expanding on the initial state. Fundamental bifurcation diagrams are given for the unit circuit and the coupled system. Some of the phenomena are confirmed by laboratory experiments.

Torus doubling and hyperchaos in a five dimensional hysteresis circuit

This article discusses a simple five dimensional autonomous circuit that includes one piecewise linear hysteresis element. We derive theoretical formulae of its three dimensional return map, its Jacobian matrix and Jacobian. Applying these to evaluate Lyapunov exponents, we clarify torus doubling route to area expanding chaos and volume expanding chaos which is a kind of hyperchaos. We also investigate basic bifurcation of these phenomena. Some attractors from the return map are verified by laboratory measurements.<<ETX>>

Stabilizing high-period orbits in chaos and generation of islands: a piecewise linear approach

This paper proposes a novel piecewise linear autonomous chaos generator and considers the following problems: (1) controlling chaos; and (2) generation of islands. The chaotic system is a novel version of the Manifold Piecewise Linear (MPL) system and its dynamics are governed by a piecewise linear map with hysteresis. It is noted that stabilizing high-period orbits is hard for the old MPL but is easy for the novel MPL because of the hysteresis effect in its return map. Islands are chaos whose support is the union of divided subintervals in the domain of the return map. Also, we have clarified interesting bifurcation phenomena for the islands.

Rigorous and realistic control of piecewise linear chaos

A simple but efficient control method of piecewise linear chaos is proposed. It operates only in a linear region and must stabilize any unstable periodic orbit in a theoretical sense. We apply the method for a hysteresis chaos generator for which some theoretical evidence for chaos can be given. An implementation example of the control method is also given.<<ETX>>

Various impulsive synchronous patterns from mutually coupled ISC chaotic oscillators

Using two chaotic oscillators, a novel mutually coupled system is constructed, where the coupling is realized by impulsive signals. The system exhibits various synchronous phenomena. We have classified basic synchronous phenomena from the system and have clarified existence regions theoretically in the parameter space. These phenomena can be verified in the laboratory.

Synchronization of chaos in simple circuits with dependent switched capacitor

This paper considers chaotic circuits that includes dependent switched capacitor (ab. DSC) and its master slave system. The DSC function is instantaneous short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically. If master chaos does not include the homoclinic orbit, the master-slave system exhibits synchronization of chaos, otherwise it exhibits the switching of them. As an example circuit, we select Wien bridge oscillator with DSC and have confirmed the theoretical results in laboratory experiments.

A hysteresis hyperchaos generator family

This article discusses a four dimensional autonomous circuit family that includes one hysteresis element. We derive theoretical formulae of the two dimensional return map, its Jacobian matrix and its Jacobian and show the following novel results: (1) classification of the phenomena by evaluation of Lyapunov exponents using the formulae; (2) period doubling route to chaos and the transition to hyperchaos via crisis; (3) basic bifurcation of these phenomena; and (4) implementation example and laboratory measurements of some attractors.