Narrow Results

The paper introduces a class of third-order nonsymmetric Cellular Neural Networks (CNNs), and shows through computer simulations that they undergo a cascade of period doubling bifurcations which leads to the birth of a large-size complex attractor. A major point is that these bifurcations and complex dynamics happen in a small neighborhood of a particular CNN with a symmetric interconnection matrix.

The paper addresses robustness of complete stability with respect to perturbations of the interconnections of nominal symmetric neural networks. The influence of the maximum neuron activation gain on complete stability robustness is discussed for a class of third-order neural networks. It is shown that high values of the gain lead to an extremely small complete stability margin of all nominal symmetric neural networks, thus allowing to conclude that complete stability robustness cannot be, in general, guaranteed.

This paper investigates the issue of robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominally symmetric interconnections. More specifically, a class of circular one-dimensional (1-D) CNNs with nearest-neighbor interconnections only, is considered. The class has sparse interconnections and is subject to perturbations which preserve the interconnecting structure. Conditions assuring that the perturbed CNN has a unique equilibrium point at the origin, which is unstable, are provided in terms of relative magnitude of the perturbations with respect to the nominal interconnection weights. These conditions allow one to characterize regions in the perturbation parameter space where there is loss of stability for the perturbed CNN. In turn, this shows that even for sparse interconnections and structure preserving perturbations, robustness of complete stability is not guaranteed in the general case.

Chaotic maps represent an effective method of generating random-like sequences, that combines the benefits of relying on simple, causal models with good unpredictability. However, since chaotic maps behavior is generally strongly dependent on unavoidable implementation errors and external perturbations, the possibility of guaranteeing map statistical robustness is of great practical concern. Here we present a technique to guarantee the independence of the first-order statistics of external perturbations, modeled as an additive, map-independent random variable. The developed criterion applies to a quite general class of maps.

Small-world networks embedded in Euclidean space represent useful cartoon models for a number of real systems such as electronic circuits, communication systems, the large-scale brain architecture and others. Since the small-world behavior relies on the presence of long-range connections that are likely to have a cost which is a growing function of the length, we explore whether it is possible to choose suitable probability distributions for the shortcut lengths so as to preserve the small-world feature and, at the same time, to minimize the network cost. The flow distribution for such networks, and their robustness, are also investigated.

In this paper, we introduce an observer-based chaotic communication system proposed by Grassi et al. to the transmitted signal of a dynamical compensator to improve the robustness of the cryptosystem. Specifically, we parameterize a synchronizer and an H_∞ synchronizer based on the robust control theory. Furthermore, we design a free parameter in the dynamics to improve the robust stability of the cryptosystem with respect to delays in the transmission line.

In this paper, the dynamical behavior of a class of third-order competitive cellular neural networks (CNNs) depending on two parameters, is studied. The class contains a one-parameter family of symmetric CNNs, which are known to be completely stable. The main result is that it is a generic property within the family of symmetric CNNs that complete stability is robust with respect to (small) nonsymmetric perturbations of the neuron interconnections. The paper also gives an exact evaluation of the complete stability margin of each symmetric CNN via the characterization of the whole region in the two-dimensional parameter space where the CNNs turn out to be completely stable. The results are established by means of a new technique to investigate trajectory convergence of the considered class of CNNs in the nonsymmetric case.

This paper addresses and reports the construction of a reconfigurable logic block that can morph between all three input, one output logic functions based on chaos computing theory. The logic block is constructed based on a discrete chaotic circuit and can emulate all three input, one output logic functions. We have derived instruction set table of this logic block from the block that can be used as a look up table to generate any special three input, one output logic function. Additionally, sensitivity of constructed logic block to noise is investigated and a method for enhancing robustness of block with respect to the environment noise is proposed and implemented. This chaotic block offers inventive approaches for constructing higher order logic functions.

In the development of Drosophila wing disc, morphogen Dpp, which is a signaling molecule from a local region and disperses into anterior and posterior compartments, builds up a gradient with precise pattern information. Experiments have demonstrated that the key genes (brk, dad, omb and sal) and phosphorylated protein (pMad), which are activated by Dpp signaling molecules and form the gradients of the corresponding proteins of these genes, direct and control the spatial pattern of the wing disc. However, the regulatory network of these genes are in complex and nonlinear interaction with upstream regulators and downstream targets. In this paper, the mathematical model is built according to the regulatory relationships of these key genes. The stabilities of the gradients of these corresponding proteins are investigated. Furthermore, numerical simulations show that these gradients are robust with respect to some major reaction rates in this regulatory network.

The hypothesis that a positive correlation exists between the complexity of a biological system, as described by its connectance, and its stability, as measured by its ability to recover from disturbance, derives from the investigations of the physiologists, Bernard and Cannon, and the ecologist Elton. Studies based on the ergodic theory of dynamical systems and the theory of large deviations have furnished an analytic support for this hypothesis. Complexity in this context is described by the mathematical object evolutionary entropy, stability is characterized by the rate at which the system returns to its stable conditions (steady state or periodic attractor) after a random perturbation of its robustness. This article reviews the analytical basis of the entropy — robustness theorem — and invokes studies of genetic regulatory networks to provide empirical support for the correlation between complexity and stability. Earlier investigations based on numerical studies of random matrix models and the notion of local stability have led to the claim that complex ecosystems tend to be more dynamically fragile. This article elucidates the basis for this claim which is largely inconsistent with the empirical observations of Bernard, Cannon and Elton. Our analysis thus resolves a long standing controversy regarding the relation between complex biological systems and their capacity to recover from perturbations. The entropy-robustness principle is a mathematical proposition with implications for understanding the basis for the large variations in stability observed in biological systems having evolved under different environmental conditions.

Supercavity can increase the velocity of underwater vehicles greatly, however the launching state of vehicle and systematic parameters often lead to unstable motion. To solve the problem, the effect of parameters and initial conditions on the stability of vehicles is studied. With two variable parameters, namely cavitation number and feedback control gain of fin deflection angle, a simple dynamic model of supercavity system is studied. The multistability is verified through simulation. Robustness of the system is also analyzed based on its basins of attraction. There are various coexisting attractors in a relatively large region of parameter space of the supercavity system, namely coexistence of a stable equilibrium point and a periodic attractor, coexistence of various periodic attractors, coexistence of a periodic attractor with a chaotic attractor and so on, which explain the effect of parameters and initial values on stability of vehicles qualitatively. In addition, without major change in cavitation number, there is a negative correlation between the robustness of the vehicle and feedback control gain of fin deflection angle. The robustness can be improved through optimization of parameters.

This paper introduces the implementation of a computational agent-based financial market model in which the system is described on both microscopic and macroscopic levels. This artificial financial market model is used to study the system response when a shock occurs. Indeed, when a market experiences perturbations, financial systems behavior can exhibit two different properties: resilience and robustness. Through simulations and different scenarios of market shocks, these system properties are studied. The results notably show that the emergence of collective herding behavior when market shock occurs leads to a temporary disruption of the system self-organization. Numerical simulations highlight that the market can absorb strong mono-shocks but can also be led to rupture by low but repeated perturbations.

Much research attention has been devoted to the investigation of how the structure of a network affects its intended performance. However, conclusions drawn from the previous studies are often inconsistent and even contradictory. In order to identify the causes of these diverse results and to explore the impact of network topology on performance, we apply the concept of bifurcation in dynamical systems and consider the effect of varying a crucial parameter for networks of different structures. In this paper, we study transmission networks and identify the capacity setting as the parameter. Upon varying this parameter, the behavioral change of the network is observed. Specifically, we focus on communication networks and power grids, and study the improvement or degradation of robustness of such networks under variation of link capacity. We observe that the effect of increasing link capacity on robustness differs for different networks, and a bifurcation point exists in some cases which divides regions of opposite robustness behavior. Our work demonstrates that capacity settings play a crucially important role in determining how network structure affects the intended performance of transmission networks, and clarifies the previous reported contradictory results.