We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and areaexpanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the p...

This paper studies a small neural network with three neurons. First, the activation function takes the sign function. Although the network is a simple hybrid systemwith all subsystems being exponentially stable, we find that it can exhibit very complex dynamics such as limit cycles and chaos. Since the sign function is a limit case of sigmoidal functions, we find that chaos robustly exists with...

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion ...

This contribution presents the results of an investigation on deterministic spatiotemporal chaos control by means of evolutionary algorithms. Three evolutionary algorithms are used for chaos control: differential evolution, self-organizing migrating algorithm and genetic algorithm. Models of spatiotemporal chaos, so called coupled map lattices, are used. The main aim of this investigation was t...

This contribution introduces an investigation on deterministic spatiotemporal chaos control based on evolutionary algorithms use. Two evolutionary algorithms are used for chaos control here: differential evolution and self-organizing migrating algorithm. Like a model of spatiotemporal chaos so called coupled map lattices are used. Main aim of this investigation was to show that evolutionary alg...

Abstract: We reveal theoretically chaos and its control in a semiconductor laser with delayed negative optoelectronic feedback. Under nonperiodic or sinusoidal period optoelectronic current, the semiconductor laser exhibits rich nonlinear dynamics. For a given coupling constant, chaos is shown in a semiconductor laser directly injected by external light. For a photoelectric delayed negative-fee...

We report experimental control of chaos in an electronic circuit at 43.9 MHz, which is the fastest chaos control reported in the literature to date. Limiter control is used to stabilize a periodic orbit in a tuned collector transistor oscillator modified to exhibit simply folded band chaos. The limiter is implemented using a transistor to enable monitoring the relative magnitude of the control ...

Chaos, control, anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor and spring for which time-delay effect is considered are studied in the paper. By applying numerical results, phase diagram and power spectrum are presented to observe periodic and chaotic motions. Linear feedback control and adaptive control algorithm are u...

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength,...

In a recent paper [Melby P, Kaidel J, Weber N, Hubler A. Adaptation to the edge of chaos in the self-adjusting logistic map. Phys Rev Lett 2000;84:5991–3], Melby et al. attempted to understand edge of chaos behaviour through a very simple model. Based on our exhaustive numerical experiments, here we show that the model, with the definition of the edge of chaos given in the paper, cannot unequiv...