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We seek solutions u ∈ ℝn to the semilinear elliptic partial difference equation -Lu + fs(u) = 0, where L is the matrix corresponding to the Laplacian operator on a graph G and fs is a one-parameter family of nonlinear functions. This article combines the ideas introduced by the authors in two papers: (a) Nonlinear elliptic partial difference equations on graphs (J. Experimental Mathematics, 2006), which introduces analytical and numerical techniques for solving such equations, and (b) Symmetry and automated branch following for a semilinear elliptic PDE on a fractal region (SIAM J. Dynamical Systems, 2006), wherein we present some of our recent advances concerning symmetry, bifurcation and automation for PDE. We apply the symmetry analysis found in the SIAM paper to arbitrary graphs in order to obtain better initial guesses for Newton's method, create informative graphics, and better understand the role of symmetry in the underlying variational structure. We use two modified implementations of the gradient Newton–Galerkin algorithm (GNGA, Neuberger and Swift) to follow bifurcation branches in a robust way. By handling difficulties that arise when encountering accidental degeneracies and higher-dimensional critical eigenspaces, we can find many solutions of many symmetry types to the discrete nonlinear system. We present a selection of experimental results which demonstrate our algorithm's capability to automatically generate bifurcation diagrams and solution graphics starting with only an edgelist of a graph. We highlight interesting symmetry and variational phenomena. [ABSTRACT FROM AUTHOR]

In the present worldwide scenario, plenty of problems arising in science and engineering which can be modeled as differential equations and out of these, autonomous system has become a subject of great interest. Several laws of physics in which time is considered as an independent variable are expressed as autonomous systems. In this paper, Runge–Kutta (RK) three-stage geometric mean method is used to solve the initial value problem arises in autonomous systems. The method is discussed in detail, convergence of method is discussed, the accuracy and efficiency of the method are proved by considering a numerical example. The result is compared to some other methods and proposed method is found to be more efficient. The detailed analysis of error estimation confirms that proposed method is more efficient as compared to other methods. [ABSTRACT FROM AUTHOR]

Crowds of people are often found in enclosed or constricted spaces. Evacuation in such situations is usually conducted calmly, but real or perceived danger may trigger panic. In panicked crowds, the interpersonal distance crowd members normally observe is often overwhelmed by the physical pressure of crowd members pushing against each other. That pressure can both slow evacuation and lead to injury or death. Models have been developed to study crowd evacuation in a range of situations. This paper describes the implementation, testing, and validation of a crowd evacuation model using Unity, a commercial computer game engine. A realistic physics-based model of crowd movement that calculates and considers the physical pressure crowd members exert on each other was implemented in Unity. The implemented model was tested under both nonpanicked and panicked scenarios; those tests exhibited known qualitative characteristics of such scenarios. The model was then quantitatively validated by comparing its results to the outcome of an actual evacuation event, the 2003 fire at The Station nightclub in Rhode Island. The implementation and validation show that Unity can be an effective tool for evacuation modeling. [ABSTRACT FROM AUTHOR]

In this paper we present a novel support vector machine (SVM) based framework for prognosis and diagnosis. We apply the framework to sparse physics data sets, although the method can easily be extended to other domains. Experiments in applied fields, such as experimental physics, are often complicated and expensive. As a result, experimentalists are unable to conduct as many experiments as they would like, leading to very unbalanced data sets that can be dense in one dimension and very sparse in others. Our method predicts the data values along the sparse dimension providing more information to researchers. Often experiments deviate from expectations due to small misalignments in initial parameters. Our method detects these outlier experiments. [ABSTRACT FROM AUTHOR]

The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries. [ABSTRACT FROM AUTHOR]

This paper proposes a new complex network: multicenter network. Coupled maps on two different types of network, coupled map lattices with nearest neighbors and multicenter network, are investigated. Both theoretical analysis and numerical simulation show that the synchronization of coupled map is much easier than that on the regular network. [ABSTRACT FROM AUTHOR]

In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a system containing the braids and extending periodically to obtain a system naturally defined on a torus and which contains the given knotted trajectories. To get explicit differential equations for dynamical systems containing the braids, we will use a certain function to define a tube neighborhood of the braid. The second one, generating chaotic systems, is realized by modeling the Smale horseshoe. [ABSTRACT FROM AUTHOR]

This paper presents the synchronization of chaotic systems. A feed-forward neural network will be employed to form the proposed neural-network-based controller to perform chaotic synchronization. Stability conditions will be derived to guarantee the system stability. The system performance will be ensured and the parameters of the neural networks can be obtained by solving the solution to the generalized eigenvalue minimization problem. A simulation example will be given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Liénard systems and their generalized forms are classical and important models of nonlinear oscillators, and have been widely studied by mathematicians and scientists. The main problem considered is the maximal number of limit cycles that the system can have. In this paper, two types of symmetric polynomial Liénard systems are investigated and the maximal number of limit cycles bifurcating from Hopf singularity is obtained. A global result is also presented. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to show that simple dissipation can bring about oscillations in certain kinds of asymptotically stable nonlinear dynamical systems; namely when the system is locally active where the dissipation is introduced. Furthermore, if these nonlinear dynamical systems are coupled with appropriate choice of diffusion coefficients, then the coupled system can exhibit spatio-temporal oscillations. The secondary purpose of this paper is to show that spatio-temporal oscillations can occur in spatially discrete reaction diffusion equations operating on the edge of chaos, provided the array size is sufficiently large. [ABSTRACT FROM AUTHOR]

Computational auditory scene analysis (CASA) has been attracting growing interest since the publication of Bregman's text on human auditory scene analysis, and is expected to find many applications in data retrieval, autonomous robots, security and environmental analysis. This paper reports on the use of Fourier transforms and wavelet transforms to produce spectral data of sounds from different sources for classification by neural networks. It was found that the multiresolution time-frequency analyses of wavelet transforms dramatically improved classification accuracy when statistical descriptors that captured measures of band limited spectral energy and temporal energy fluctuation were used. [ABSTRACT FROM AUTHOR]

It is known that a two-spin system with four energy levels can be used to realize a two-qubit quantum gate. A feasible realization of quantum gates should rely on stable quantum mechanical states. An example of such states are edge states which arise around regions with high potential in a strong magnetic field. In this paper we show that certain edge states around a pair of antidots may be suitable for quantum gate implementation. [ABSTRACT FROM AUTHOR]

Spatial prediction needs to account for spatial information, which makes conventional radial basis function (RBF) networks inappropriate, for they assume independent and identical distribution. In this paper, we fuse spatial information at different layers of RBF. Experiments show fusion at hidden layer gives the best result and suggest that the optimal value is around one for the coefficient, which is used in the linear combination at the output layer. [ABSTRACT FROM AUTHOR]

Concepts in a certain domain of science are linked via intrinsic connections reflecting the structure of knowledge. To get a qualitative insight and a quantitative description of this structure, we perform empirical analysis and modeling of the network of scientific concepts in the domain of physics. To this end, we use a collection of manuscripts submitted to the e-print repository arXiv and the vocabulary of scientific concepts collected via the ScienceWISE.info platform and construct a network of scientific concepts based on their co-occurrences in publications. The resulting complex network possesses a number of specific features (high node density, dissortativity, structural correlations, skewed node degree distribution) that cannot be understood as a result of simple growth by several commonly used network models. We show that the model based on a simultaneous account of two factors, growth by blocks and preferential selection, gives an explanation of empirically observed properties of the concepts network. [ABSTRACT FROM AUTHOR]

Maximum likelihood method for estimating parameters of Bayesian networks (BNs) is efficient and accurate for large samples. However, the method suffers from overfitting when the sample size is small. Bayesian methods, which are effective to avoid overfitting, present difficulties for determining optimal hyperparameters of prior distributions with good balance between theoretical and practical points of view when no prior knowledge is available. As described in this paper, we propose an alternative estimation method of the parameters on BNs. The method uses a principle, rooted in thermodynamics, of minimizing free energy (MFE). We define internal energies, entropies, and temperature, which constitute free energies. Especially for temperature, we propose a "data temperature" assumption and some explicit models. This approach can treat the maximum likelihood principle and the maximum entropy principle in a unified manner of the MFE principle. For assessments of classification accuracy, our method shows higher accuracy than that obtained using the Bayesian method with normally recommended hyperparameters. Moreover, our method exhibits robustness for the choice of introduced hyperparameters. [ABSTRACT FROM AUTHOR]

This paper introduces a modified Chua's system which is a smooth four-dimensional continuous-time autonomous chaotic system with a cubic nonlinearity. Some dynamical behaviors of this 4-D Chua's system are further investigated by means of Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations and calculated Lyapunov exponents. Moreover, using RC-opamp and analog multiplier we describe a simple electronic circuit for hardware implementation of the 4-D Chua's system which differ from previously reported Chua's circuits. Various attractors of experimental results from this chaotic oscillator are in good agreement with theoretical analysis. In particular, based on the approximation theory of fractional-order operator, a relevant analog circuit diagram of this fractional-order modified Chua's system is designed with α = 0.9. Observation results demonstrate that chaos exists indeed in this fractional-order modified Chua's system with an order as low as 3.6. This fractional-order oscillation circuit, for the first time in the literature, realizes high-dimensional Chua's chaotic system. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the dynamical properties of a Holling-type II predator–prey system with constant rate harvesting. It is shown that the model has at most three equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the degenerate Bogdanov–Takens bifurcation of codimension 3, the supercritical and subcritical Hopf bifurcation, the generalized Hopf bifurcation. These results reveal far richer dynamics than that of the model with no harvesting. [ABSTRACT FROM AUTHOR]

In this paper, we use the method of displacement functions to study the existence, stability and bifurcation of periodic solutions of scalar periodic impulsive differential equations. We obtain some new and interesting results on saddle-node bifurcation and double-period bifurcation of periodic solution. [ABSTRACT FROM AUTHOR]

A modified generalized Lorenz system in a canonical form extended from the generalized Lorenz system is proposed in this paper. This novel system has a folded factor and can display complex 2-scroll folded attractors and 1-scroll folded attractors at different parameter values. Three typical normal forms, called Lorenz-like, Chen-like and Lü-like chaotic system respectively, of three-dimensional quadratic autonomous chaotic systems are derived, and their dynamical behaviors are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping and phase portrait, etc. Of particular interest is the fact that the folded factor makes Chen-like and Lü-like chaotic systems exhibit complicated nonlinear dynamical phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we study global stabilization and synchronization of n-scroll chaotic attractors for a modified Chua's circuit with hyperbolic tangent function using feedback control strategy. In particular, for any given equilibrium point of the modified Chua's circuit, we design simple and explicit controllers to globally exponentially stabilize the system. Simple controllers are also designed to globally exponentially synchronize two modified Chua's circuits. In addition to the theoretical analysis, numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers a 2-station-5-class re-entrant line with infinite supply of work. We obtain the necessary and sufficient condition for its corresponding fluid model to be stable. As an application of the result, the positive Harris recurrence of the 2-station-5-class re-entrant line is established via the fluid model. [ABSTRACT FROM AUTHOR]

In this paper we explore the design of microwave-based structures that can enhance the interaction of electromagnetic fields with cold-atom ensembles, leading to novel sensing modalities based on the quantum-mechanical behavior of these systems. In particular, we discuss electromagnetically-induced transparency in a single uncondensed cold-atom cloud, and a two-cloud version of a SQUID, where the clouds are BEC's and take the place of the weakly coupled superconductors. These systems are both promising candidates for use in the high-precision detection of chemical contaminants. [ABSTRACT FROM AUTHOR]

In this preface we propose a synthetic survey of the main ideas which are in our aim at the origin of the "Physics and the City" Symposium (Bologna–Italy, 15–17 December 2005). These ideas are developed from different point of view in the following collected papers, also with different scientific languages, from the sociological or planning to the mathematical or physical ones. Very schematically we think that the present proceedings could prefigure the emergence of a new "science of the city", really multidisciplinary and with possible spin-off on every single science concerned. Moreover with a large range of possible applications to the actual social life, in order to contribute to a better quality of life. Surely we are at the beginning and the topology of this "science of the city" it is not still well defined, but as H. Poincaré said: Pour obtenir un résultat qui ait une valeur réelle, il ne suffit pas de mettre les choses en ordre; ce n'est pas seulement l'ordre, c'est l'ordre inattendu qui vaut quelque chose. [ABSTRACT FROM AUTHOR]

In this paper we quantify our limited information horizon, by measuring the information necessary to locate specific nodes in a network. To investigate different ways to overcome this horizon, and the interplay between communication and topology in social networks, we let agents communicate in a model society. Thereby they build a perception of the network that they can use to create strategic links to improve their standing in the network. We observe a narrow distribution of links when the communication is low and a network with a broad distribution of links when the communication is high. [ABSTRACT FROM AUTHOR]

In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with polynomial perturbations of degree n have at most n(n + 1)/2 - 1 limit cycles near a center point. We also obtain some new results for Lienard systems by applying our main theorems. [ABSTRACT FROM AUTHOR]

In this paper we study the nonchaotic and chaotic behavior of all 3D conservative quadratic ODE systems with five terms on the right-hand side and one nonlinear term (5-1 systems). We prove a theorem which provides sufficient conditions for solutions in 3D autonomous systems being nonchaotic. We show that all but five of these systems: (15a, 15b), (18b), (41)(A = ∓1), (43b), and (49a, 49b) are nonchaotic. Numerical simulations show that only one of the five systems, (43b), really appears to be chaotic. If proved to be true, it will be the simplest ODE system having chaos. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a type of differential systems which appear usually in the study of the Hamiltonian systems with two degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near to the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear three-body problem. [ABSTRACT FROM AUTHOR]

In this paper, the problem of limit cycles bifurcated from the equator for a cubic polynomial system is investigated. The best result so far in the literature for this problem is six limit cycles. By using the method of singular point value, we prove that a cubic polynomial system can bifurcate seven limit cycles from the equator. We also find that a rational system has an isochronous center at the equator. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the vibration, buckling and dynamic instability behavior of laminated composite, cross-ply, doubly-curved panels with a central circular hole subjected to in-plane static and periodic compressive loads. A generalized shear deformable Sanders' theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. Bolotin's approach is used for studying the dynamic instability regions of doubly-curved panels. The effects of non-uniform edge loads, curvature with different cutout ratios, static and dynamic load factors, and lamination parameters on curved panels are investigated with the results discussed. [ABSTRACT FROM AUTHOR]

In this paper we consider the longitudinal vibrations of bimodular rods. After proving the equivalence between the entropy condition and Lax condition (whenever this latter is applicable), we go on to consider the Riemann problem and prove that a unique solution always exists except for the special case of no-tension materials. This procedure allows for easy determination of the explicit solution. [ABSTRACT FROM AUTHOR]

When using the ordered weighted average operator, it can happen that one wants to optimize the variability (measured by the entropy (maximal) or by the variance (minimal)) of the weights while keeping the orness of this operator at a fixed level. This has been considered by several authors. Dually, there might be some contexts where one wishes to maximize the orness while guaranteeing some fixed variability. In this paper, we present two algorithms for finding such weights, when the variability is captured by the entropy and by the variance. [ABSTRACT FROM AUTHOR]

The paper presents a simulation study of the physics and performance of novel asymmetric tunneling solutions for the sub-100nm MOSFET technology. Two device structures have been investigated: Schottky Tunneling Source MOSFET and band-to-band P+-N+ Tunneling Source MOSFET. The Schottky MOSFET exhibits degraded Ion and subthreshold swing (in spite of improved DIBL). On the other hand, the novel PNPN MOSFET shows high Ion/Ioff and steep subthreshold behavior. [ABSTRACT FROM AUTHOR]

This paper describes work on methods that evaluate algebraic solutions to word problems in physics. Many current tutoring systems rely on substantial scaffolding and consequently require students to completely describe every variable used in the solution. A heuristic, based on constraint propagation, capable of inferring the description of variables (i.e., the possible dimensions and physics concepts) is shown to be highly reliable on three real world data sets, one covering a few problems with a small number of student answers and two others covering a large class of problems (~100) with a large number of student answers (~11,000). The heuristic uniquely determines the dimensions of all the variables in 91–92% of the equation sets. By asking the student for dimension information about one variable, an additional 3% of the sets can be determined. An ITS tutoring system can use this heuristic to reason about a student's answers even when the scaffolding and context are removed. [ABSTRACT FROM AUTHOR]

We investigate the emergence of power-law scalings in genealogical trees. Especially, we study the topological properties of genealogical trees both in the neutral evolution and the selective evolution. In all instances, we observe that the topologies of these trees are well described by a power-law scaling $C_k\sim A_k^\eta$, where Ak is the number of nodes which are direct or indirect descendants of node k and Ck=∑jAj where the sum is taken over all nodes that contribute to Ak. This relation is well known in transportation networks as well as in metabolic networks, and it is referred to as allometric scaling. Furthermore, we observe a slight dependence of the scaling exponent η on the intensity of selection. [ABSTRACT FROM AUTHOR]

An interview with International Young Physicists' Tournament (IYPT) 2010 winners Li Kewei, Lin Jiahuang and Kang Zi Yang is presented. When asked about the impact of IYPT on their participation in other physics Olympiad, they talked about being exposed to thermodynamics, optics and electromagnetism. They mentioned the challenge they faced during IYPT and offered advice on students embarking on IYPT 2011.

Recent findings suggest that processes such as the excitonic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, master-equation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining a local description of the complex network of molecules involved in the transport, say through a tight-binding approach. Interestingly, the continuous time random walk (CTRW) picture, widely employed in describing transport in random environments, can be mathematically reformulated to yield a quantum-mechanical Hamiltonian of tight-binding type; the procedure uses the mathematical analogies between time-evolution operators in statistical and in quantum mechanics: The result are continuous-time quantum walks (CTQWs). However, beyond these formal analogies, CTRWs and CTQWs display vastly different physical properties. In particular, here we focus on trapping processes on a ring and show, both analytically and numerically, that distinct configurations of traps (ranging from periodical to random) yield strongly different behaviors for the quantal mean survival probability, while classically (under ordered conditions) we always find an exponential decay at long times. [ABSTRACT FROM AUTHOR]

We show how ordinary, finite-temperature tools of Statistical Mechanics can be used to detect quantum phase transitions in many-body systems. In particular, statistical correlations exhibit a quite idiosyncratic behavior at the critical interaction-strengths. Moreover, what one may call "soft quantum phase-transitions" (crossings of excited states) are characterized by the rather special way of vanishing that these correlations adopt. [ABSTRACT FROM AUTHOR]

We present an analysis of temperature fluctuations in a horizontal round heated turbulent jet. Instantaneous temperature time series were recorded at several points along a horizontal line in the plane of symmetry of the jet. The time series are analyzed using Recurrence Quantification Analysis (RQA). The variation of characteristic RQA measures is associated with and interpreted via the transitions of the physical state of the fluid from the fully-turbulent flow near the jet centerline to the transitional flow near the boundary of the jet. [ABSTRACT FROM AUTHOR]

The identification of community structures in networks is investigated within a framework based on the concepts of higher order neighborhoods and neighborhood matrix $\hat{M}$. This procedure is of relevance especially for networks representing evolutionary situations, since several evidences show that they are assembled from pre-existing smaller structures, rather than by the mere adhesion of individual nodes. We proceed within the successive elimination of the links with largest betweenness degree. The effect of erasing a link at step k is quantified by the distance between $\hat{M}^{k-1}$ and $\hat{M}^{k}$, which describe the network neighborhoods prior and after the kth link elimination. For modular networks, this measure is characterized by a very long sequence of sharp peaks, following a much more complete cascade of cluster splitting. The evidences indicate that this method identifies a more precise description of smaller communities splitting than the one based on modularity function. [ABSTRACT FROM AUTHOR]

Variational principles and partial differential equations have proved to be fundamental elements in the mathematical modeling of extended systems in physics and engineering. Of particular interest are the equations that arise from a free energy functional. Recently variational principles have begun to be used in Image Processing to perform basic tasks such as denoising, debluring, etc. Great improvements can be achieved by selecting the most appropriate form for the functional. In this article we show how these ideas can be applied not just to scalar fields (i.e. grayscale images) but also to curved manifolds such as the space of orientations. This work is motivated by the denoising of images acquired with Magnetic Resonance scanners using diffusion-sensitized magnetic gradients. [ABSTRACT FROM AUTHOR]

Detection of gaseous effluent plumes from airborne platforms provides a unique challenge to the remote sensing community. The measured signatures are a complicated combination of phenomenology including effects of the atmosphere, spectral characteristics of the background material under the plume, temperature contrast between the gas and the surface, and the concentration of the gas. All of these quantities vary spatially further complicating the detection problem. In complex scenes simple estimation of a “residual” spectrum may not be possible due to the variability in the scene background. A common detection scheme uses a matched filter formalism to compare laboratory-measured gas absorption spectra with measured pixel radiances. This methodology can not account for the variable signature strengths due to concentration path length and temperature contrast, nor does it take into account measured signatures that are observed in both absorption and emission in the same scene. We have developed a physics-based, forward model to predict in-scene signatures covering a wide range in gas / surface properties. This target space is reduced to a set of basis vectors using a geometrical model of the space. Corresponding background basis vectors are derived to describe the non-plume pixels in the image. A Generalized Likelihood Ratio Test is then used to discriminate between plume and non-plume pixels. Several species can be tested for iteratively. The algorithm is applied to airborne LWIR hyperspectral imagery collected by the Airborne Hyperspectral Imager (AHI) over a chemical facility with some ground truth. When compared to results from a clutter matched filter the physics-based signature approach shows significantly improved performance for the data set considered here. [ABSTRACT FROM AUTHOR]

We illustrate a physicist's point of view on the rise of Complexity Science. We analyze the change of meaning of the word "prediction" in the passage from Laplace's determinism to Statistical Mechanics. We show that an analogous change in the meaning of prediction is at the base of the Physics of complex systems. [ABSTRACT FROM AUTHOR]

A particularly simple and mathematically elegant example of chaos in a three-dimensional flow is examined in detail. It has the property of cyclic symmetry with respect to interchange of the three orthogonal axes, a single bifurcation parameter that governs the damping and the attractor dimension over most of the range 2 to 3 (as well as 0 and 1) and whose limiting value b = 0 gives Hamiltonian chaos, three-dimensional deterministic fractional Brownian motion, and an interesting symbolic dynamic. [ABSTRACT FROM AUTHOR]

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for continuous-time neural networks under pure structural variations with impulsive perturbations: \[ \left\{\begin{array}{l} \displaystyle\frac{du_{j}(t)}{dt} = -b_{j}u_{j} (t) + \displaystyle\sum_{k=1}^{n}A_{jk}s_{jk}(t)g_{k}(u_{k}(t)) + U_{j} (t), \quad t>0, \enskip t\neq t_i,\\[15pt] \Delta u_{j}(t_i)=u_{j}(t_{i}^{+})-u_{j}(t_{i}^{-})=I_{j}(u_{j}(t_i)),\quad i=1,2,\ldots; \enskip d j=1,2,\ldots,n. \end{array}\right. \] The results extend earlier ones where impulses are absent. Further, using numerical simulation method the influences of the impulsive perturbations on the inherent oscillation are investigated. [ABSTRACT FROM AUTHOR]

The dynamics of a Mackey–Glass equation with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Global existence of periodic solutions are established using a global Hopf bifurcation result due to Wu [1998] and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney [1994]. [ABSTRACT FROM AUTHOR]

Active Walk (AW) is a paradigm for self-organization and pattern formation in simple and complex systems, originated by Lam in 1992. In an AW, the walker changes the deformable landscape as it walks, and is influenced by the changed landscape in choosing its next step. Active walk models have been applied successfully to various biological, physical, geological and economic systems from both the natural and social sciences. More recently, it has been used to model human history. In Part I of this review, the birth of the AW paradigm, its basic concepts and formulations, a solvable two-site model, and the experiments and AW modeling of surface-reaction filamentary patterns are presented. Part II here continues with properties of AW, and applications of AW in nonliving and living systems — including those from the social sciences and human history. (In particular, unsuspected quantitative laws and a prediction about the Chinese history are given.) A comment on the relationship between physics, social science and complex systems is provided. The review concludes with open problems in the form of workable research projects and general discussions. [ABSTRACT FROM AUTHOR]

Small, discrete, corrective adjustments to foot geometry in a class of bipedal passive walkers are employed to affect the local stability properties of a periodic reference gait. It is demonstrated that successful stabilization can be accomplished for otherwise strongly unstable motions of vertically constrained as well as entirely unconstrained model mechanisms. In particular, recent results by the authors on stabilization of repetitive motion in hybrid dynamical systems are implemented to formulate a rigorous analytical methodology for predicting the stability characteristics of the controlled system. It is demonstrated that these predictions can be explicitly obtained based entirely on knowledge of the local stability properties of the reference motion in the absence of control. [ABSTRACT FROM AUTHOR]

This study investigates the error which occurs when numerically integrating the equation of motion of a single degree of freedom system excited by a harmonic force near resonance. The Constant Average Acceleration method was considered in particular as it features in many finite element software packages. It was found that a considerable error in the calculated responses occurs in systems with low damping due to the well known phenomenon of period elongation. However, the error is reduced for systems with higher damping and/or when smaller time step is used. With regard to this, recommendations are given as to the time steps required to obtain solutions with a pre-defined level of accuracy. [ABSTRACT FROM AUTHOR]

We study Cantor staircases arising from different problems in Physics. Each staircase is endowed with the Farey structure in the vertical axis, the underlying cantordust set Ω having a fractal dimension strictly between 0 and 1. We find that length and distribution of stairsteps follow hyperbolic laws related to the Poincaré measure in the hyperbolic half-plane. The geometry of the underlying Ω is studied with the same tools. [ABSTRACT FROM AUTHOR]