In this paper, an algorithm for computing heteroclinic orbits of nonlinear systems, which can have several hyperbolic equilibria, is suggested and analyzed both analytically and numerically. The method is based on a representation of the invariant manifold of a hyperbolic equilibrium via a certain exponential series expansion. The algorithm for computing the series coefficients is derived and the uniform convergence of the series is theoretically proved. The algorithm is then applied to computing heteroclinic orbits numerically in the generalized Lorenz system, thereby theoretically justifying the previously demonstrated existence of chaotic oscillations in this important class of dynamical systems.
When multi-agent systems are equipped with embedded microprocessors of limited resources, it is important to design an appropriate real-time scheduling of control tasks. In this paper, we examine the synthesis of event-triggered information transmission and distributed estimation for a tracking control problem of leader-follower multi-agent systems. For a second-order leader-follower multi-agent system, we use a decentralized event-triggered strategy in the dynamic tracking control design. Then, we analyze the input-to-state stability of the closed-loop multi-agent system with the proposed event-triggered tracking control. Finally, we present a numerical simulation to validate the proposed design.
Describes a continuous differential equation model of the interaction dynamics of HIV-1 and CD4 and CD8 lymphocytes in the human body. The authors demonstrate several methods of stable control of the HIV-1 population using an external feedback control term that is analogous to the introduction of a therapeutic drug regimen. They also show how the immune system components can be bolstered against the virus through a feedback control approach.
This invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first -- cellular nonlinear networks, nonlinear circuits and cellular automata -- deals with Chua's Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua's circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua's views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into 'ancient memristors', analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book. The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science. The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua's circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike.
We give certain sequential and parallel algorithms and their computational analysis for signal decomposition and reconstruction based on wavelets. The signal decomposition (respectively, reconstruction) process is separated into two stages: the first is the preprocessing stage where certain constants are computed for implementation to prepare for the second stage in which signal decomposition (respectively, reconstruction) is performed. In the decomposition (respectively, reconstruction) stage, the input signal is transformed via different methods to compute the output signal without changing the setup initialized in the preprocessing stage. We describe certain sequential algorithms for both the preprocessing and the decomposition (respectively, reconstruction) stages, and parallel algorithms for the latter. The algorithms are finally illustrated for compactly supported spline-wavelets and are analyzed in detail in terms of the required arithmetic operations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
In social gaming networks, the current research focus has been on the origin of widespread reciprocal behaviors when individuals play non-cooperative games. In this paper, we investigate the topological properties of unfavorable individuals in evolutionary games. The unfavorable individuals are defined as the individuals gaining the lowest average payoff in a round of game. Since the average payoff is normally considered as a measure of fitness, the unfavorable individuals are very likely to be eliminated or change their strategy updating rules from a Darwinian perspective. Considering that humans can hardly adopt a unified strategy to play with their neighbors, we propose a divide-and-conquer game model, where individuals can interact with their neighbors in the network with appropriate strategies. We test and compare a series of highly rational strategy updating rules. In the tested scenarios, our analytical and simulation results surprisingly reveal that the less-connected individuals in degree-heterogeneous networks are more likely to become the unfavorable individuals. Our finding suggests that the connectivity of individuals as a social capital fundamentally changes the gaming environment. Our model, therefore, provides a theoretical framework for further understanding the social gaming networks.
Traditionally, marine traffic congestion degree in restricted waters is usually deduced from traffic volume or traffic density. Both of which, however, can not be easily and accurately determined and can not fully reflect the traffic congestion degree. This paper uses the concept of main traffic flow velocity, which varies with the main traffic congestion from a statistics view, to determine the main traffic congestion degree in restricted waters. Main traffic flow velocity can be calculated by averaging the speeds of all ships equipped with an AIS transponder if the percentage of these ships over all vessels in the main traffic is great enough and they are well-distributed, and a fuzzy relationship is established to determine the traffic congestion degree under varying main traffic flow velocity. The concept of main traffic flow velocity provides a more intuitive and accurate way to evaluate the main traffic congestion degree of restricted waters than traffic density and traffic volume in certain situations, and can be easily implement.
As an important part of many processors's floating point unit, fused multiply-add unit performs a multiplication followed immediately by an addition. In IBM POWER6 microprocessor's fused multiply-add unit, a fast 128-bit floating-point end-around-carry (EAC) adder is proposed. Very few algorithmic details exist in today's literature about this adder. In this study, a complete designed EAC adder that can work independently as a regular adder is proposed. Details about the proposed EAC adder's arithmetic algorithms are described. In IBM's original EAC adder, the Kogge–Stone tree has been chosen for its high performance on ASIC technology. In this study, the authors present a comparative study on different parallel prefix trees which are used in the design of our new EAC adder targeting field programmable gate array (FPGA) technology. Our study highlights the main performance differences among 14 different architecture configurations focusing on the area requirements and the critical path delay. The experimental results show that there is one architecture configuration with the lower area requirement and the higher performance.
This paper introduces a generalized stability with respect to a transformation (GST) for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). Some constructive theorems provide general representations of GST in both CDADS and CCADS. Using these theorems, one can design GST-based CADS and CCADS via appropriate transformations. As examples, the results are applied to autonomous and nonautonomous coupled discrete and differentiable Lorenz cellular neural network (CNN) CADS and CCADS; differentiable Chen CNN CCADS, and discrete sine-function CNN CADS. Extensive numerical simulations show their complex dynamic behaviors. The established theorems provide insights for better understanding of some new phenomena of complex discrete and continuously-differentiable networks.
