Strong Attractor Research Articles

The Call of the Crowd: Event Participation in Location-Based Social Services

Understanding the social and behavioral forces behind event participation is not only interesting from the viewpoint of social science, but also has important applications in the design of personalized event recommender systems.This paper takes advantage of data from a widely used location-based social network, Foursquare, to analyze event patterns in three metropolitan cities. We put forward several hypotheses on the motivating factors of user participation and confirm that social aspects play a major role in determining the likelihood of a user to participate in an event. While an explicit social filtering signal accounting for whether friends are attending dominates the factors, the popularity of an event proves to also be a strong attractor. Further, we capture an implicit social signal by performing random walks in a high dimensional graph that encodes the place type preferences of friends and that proves especially suited to identify relevant niche events for users. Our findings on the extent to which the various temporal, spatial and social aspects underlie users' event preferences lead us to further hypothesize that a combination of factors better models users' event interests. We verify this through a supervised learning framework. We show that for one in three users in London and one in five users in New York and Chicago it identifies the exact event the user would attend among the pool of suggestions.

Strong Pullback Attractors for Nonautonomous Suspension Bridge Equations

We prove the existence of a pullback 𝒟-attractor in DA×V for the nonautonomous suspension bridge equations.

Global attractor for the Kirchhoff type equations with strong nonlinear damping and supercritical nonlinearity

Abstract The paper studies the existence of global strong attractor for the Kirchhoff type equations with strong nonlinear damping and supercritical nonlinearity u t t − σ ( ‖ ∇ u ‖ 2 ) Δ u t − ϕ ( ‖ ∇ u ‖ 2 ) Δ u + f ( u ) = h ( x ) . It proves that in strictly positive stiffness factors and supercritical nonlinearity case, there exists a global finite-dimensional attractor in the natural energy space endowed with strong topology (rather than partially strong topology). The result extends the recent one achieved by Chueshov (2012).

Long‐term dynamics of macrophyte dominance and growth‐form types in two north‐west German lowland streams

Summary Continuous multiyear data sets can help to detect long‐term trends and allow predictions with respect to environmental and biological variables. While the use of taxon‐based approaches for biomonitoring of watercourses is well established, little information exists concerning long‐term variability of dominance and growth form composition of aquatic macrophyte communities. We analysed patterns in dominance and growth forms of macrophytes over a period of 21 years in relation to changes in water chemistry, disturbance regime and extreme weather conditions in two reference streams in the north‐west German lowlands. Rank–abundance curves of annual observations indicated five core species. The pattern of abundance resembled a broken‐stick rather than a log‐normal distribution. The core species, which reached both the highest absolute and average cover values, were Sparganium emersum, Elodea canadensis, Callitriche hamulata, Potamogeton natans and Ranunculus peltatus. An analysis of change in dominance showed that in 67.5% of all observed cases, the same species became dominant in the subsequent year. Sparganium emersum (80.6%) and E. canadensis (68.8%) were the most successful species in retaining their relative dominance. Calculation of transition probabilities showed a strong attractor function of states dominated by Sparganium and Elodea. However, dominance patterns broke down over time and after 20 years, only one of the sites still showed the same dominance type. On average, dominance was preserved for around 4 years. Reaches were mostly dominated by six growth forms, namely vallisnerids, potamids, peplids, nymphaeids, myriophyllids and graminids. In each reach, two, three or five growth forms shared the highest cover percentages. An analysis of traits of successfully established and dominant species identified three strategies: a facultative wintergreen growth habit in combination with effective means of vegetative reproduction; strong maintenance traits (in particular rhizomes); short‐life span in combination with seed and turion production. Strong oscillations of growth form types were observed. Six growth form clusters were defined, up to four of which may occur in one reach. Most frequent clusters were one characterised by strong vallisnerid dominance and another characterised by dominant potamids with peplids and myriophyllids. Both clusters showed the highest frequencies, durations and transition probabilities from other clusters. On average, growth form clusters persisted for 4.5 years. An analysis of the influence of environmental factors on growth form dynamics showed that chemical and physical parameters distinguish the sample sites but cannot explain the observed changes. We conclude that dynamics of species dominance as well as the occurrence of growth form assemblages are not controlled by physicochemical environmental factors such as nutrient composition at the scale of observation in this type of river. Instead, stochastic interactions between species characteristics and single disturbance events or weather extremes must be assumed. Implications for nature conservation, biomonitoring and reconstruction of reference sites are discussed. Continuous multiyear sampling is essential to understand the temporal behaviour of the system.

SOME ATTRACTORS IN THE EXTENDED COMPLEX LORENZ MODEL

We address the question of finding the attractors of the extended complex Lorenz model (ℂLM), which is obtained by extending the space from ℝ3 to ℂ3, and defining the model by the same equations as the classical Lorenz model (LM). We have numerical evidence of two strong attractors unrelated to the Lorenz attractor. We calculate its Lyapunov exponents and show that two of them are 0, and the other four are double and negative. Hence the attractors are nonchaotic. We show that they have a quasi-periodic nature. To decipher the structure of these attractors, we introduce the imaginary Lorenz model (𝕀LM), which is defined in the same space ℂ3 by multiplying with [Formula: see text] the Lorenz equations. Both models locally commute, and with its help we account for the double Lyapunov exponent 0 and show evidence that the basin of attraction of each attractor is a big open set of ℂ3. The chaotic limit set Lℂ ⊂ ℂ3 obtained from the classical Lorenz attractor L0 of (LM) by moving it with the (𝕀LM) has two positive Lyapunov exponents, but only captures a set of 6D-volume 0 in its basin of attraction. Hence this attractor may be hyperchaotic in ℝ5.

Attractivity, multistability, and bifurcation in delayed Hopfieldʼs model with non-monotonic feedback

For a system of delayed neural networks of Hopfield type, we deal with the study of global attractivity, multistability, and bifurcations. In general, we do not assume monotonicity conditions in the activation functions. For some architectures of the network and for some families of activation functions, we get optimal results on global attractivity. Our approach relies on a link between a system of functional differential equations and a finite-dimensional discrete dynamical system. For it, we introduce the notion of strong attractor for a discrete dynamical system, which is more restrictive than the usual concept of attractor when the dimension of the system is higher than one. Our principal result shows that a strong attractor of a discrete map gives a globally attractive equilibrium of a corresponding system of delay differential equations. Our abstract setting is not limited to applications in systems of neural networks; we illustrate its use in an equation with distributed delay motivated by biological models. We also obtain some results for neural systems with variable coefficients.

Variability and stability in Chinese syntax

In this study I examine a large number of verbalizations in the Chinese Pear narratives and find that for each scene examined there is usually one or at most two favored and stabilized verbalizations, with variability around the stabilized forms. These favored verbalizations are the preferred states of the system for expressing concurrent events, transfer of objects, perfectivity in event construal etc., and they may be thought of as strong attractors in the behavior space in terms of complexity theory. These attractors exert a force on the grammatical system, and impose a frame on them and model the development of new forms. Further research in Chinese grammar into the wide ranging, dynamic and systematic variability as well as stability within and across individuals is urged.

Strong Attractor of Beam Equation with Structural Damping and Nonlinear Damping

This paper is mainly concerned with the existence of a global strong attractor for the nonlinear extensible beam equation with structural damping and nonlinear external damping. This kind of problem arises from the model of an extensible vibration beam. By the asymptotic compactness of the related continuous semigroup, we prove the existence of a strong global attractor which is connected with phase spaceD(Δ2)×H01(Ω)∩H2(Ω).

How psychological momentum changes in athletes during a sport competition

ObjectivesThe present research sought to examine changes in psychological momentum (PM) during sport competitions through the lens of a dynamical systems approach. DesignMale regional-level cyclists competed in cycling duels on home trainers. MethodImages of moving avatars of the cyclists were projected on a wall, and were manipulated so that one cyclist was exposed to an ascending performance scenario (i.e., positive momentum) and the other to a descending performance scenario (i.e., negative momentum). Every 3 min, the cyclists answered PM items by using a keyboard that was placed on the handlebars of their bicycles. Additionally, exerted power was continuously recorded. ResultsResults revealed an asymmetrical critical boundary pattern for PM perceptions indicating that negative PM was triggered more easily than positive PM. Exerted power was generally higher during the negative momentum scenario than during the positive momentum scenario. In addition, exerted power slowly decreased over both momentum scenarios, and this decrease was faster at the very beginning of the negative momentum scenario. ConclusionResults indicate that PM perceptions possess the dynamical properties of nonlinearity and history-dependence. Moreover, the finding that exerted power was higher in the negative momentum scenario was interpreted as a resistance behavior that occurs while experiencing negative momentum. The anticipated decreases in both exerted power and PM perceptions in the negative momentum scenario converge to support the notion that negative PM is a stronger attractor than positive PM. The present study confirms that PM is a dynamical phenomenon and offers fruitful avenues for future research.

Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations

A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and deducing suitable a-priori estimates. If a viscosity term is added and additional conditions on the nonlinear terms are assumed, then it is proved that any weak solution becomes instantaneously strictly positive. This in particular implies uniqueness for strictly positive times and further time-regularization properties. The long-time behavior of the problem is also investigated and the existence of trajectory attractors and, under more restrictive conditions, of strong global attractors is shown.

Terminations VI and VIII (∼ 530 and ∼ 720 kyr BP) tell us the importance of obliquity and precession in the triggering of deglaciations

Abstract. The main variations of ice volume of the last million years can be explained from orbital parameters by assuming climate oscillates between two states: glaciations and deglaciations (Parrenin and Paillard, 2003; Imbrie et al., 2011) (or terminations). An additional combination of ice volume and orbital parameters seems to form the trigger of a deglaciation, while only orbital parameters seem to play a role in the triggering of glaciations. Here we present an optimized conceptual model which realistically reproduce ice volume variations during the past million years and in particular the timing of the 11 canonical terminations. We show that our model looses sensitivity to initial conditions only after ∼200 kyr at maximum: the ice volume observations form a strong attractor. Both obliquity and precession seem necessary to reproduce all 11 terminations and both seem to play approximately the same role. More precisely, obliquity plays a fundamental role in the triggering of termination VI (~530 kyr BP), while precession plays a fundamental role in the triggering of termination VIII (~720 kyr ago).

Global Attractor for a Class of Coupled Nonlinear Schrödinger Equations

In this paper, the long time behavior of solution for a class of coupled nonlinear Schrodinger equation with zero order dissipation is studied. We first construct the global weak attractor for this system in H2 per(?) H2 per(?). And then by exact analysis of the energy equation, we shown that the global weak attractor is actually the global strong attractor in H2 per(?) H2 per(?). We also estimate the uniform Lyapunov exponents on the attractor, which allows us to prove its finite dimensional property.

The Attractors in the Complex Lorenz Model

We address the question of finding the attractors of the complex Lorenz model (CLM), which is obtained by extending the space from ℝ3 to ℂ3, and defining the model by the same equations as the classical Lorenz model (LM). We have numerical evidence of 2 strong attractors un-related to the Lorenz attractor. We calculate its Lyapunov exponents and show that 2 of them are 0, and the other 4 are double and negative. Hence the attractors are non-chaotic. We show that they have a quasi-periodic nature. To decipher the structure of these attractors, we introduce the imaginary Lorenz model (ILM), which is defined in the same space ℂ3 by multiplying with √−1 the Lorenz equations. Both models locally commute, and with its help we account for the double Lyapunov exponent 0 and show that the basin of attraction of each attractor is a big open set of ℂ3. The chaotic limit set Lℂ ⊂ ℂ3 obtained from the classical Lorenz attractor L0 of (LM) by moving it with the (ILM) has 2 positive Lyapunov exponents, but only captures a set of 6D-volume 0 in its basin of attraction.

INTERMITTENCY AND INTERIOR CRISIS AS ROUTE TO CHAOS IN DYNAMIC WALKING OF TWO BIPED ROBOTS

Recently, passive and semi-passive dynamic walking has been noticed in researches of biped walking robots. Such biped robots are well-known that they demonstrate only a period-doubling route to chaos while walking down sloped surfaces. In previous researches, such route was shown with respect to a continuous change in some parameter of the biped robot. In this paper, two biped robots are introduced: the passive compass-gait biped robot and the semi-passive torso-driven biped robot. The period-doubling scenario route to chaos is revisited for the first biped as the ground slope changes. Furthermore, we will show through bifurcation diagram that the torso-driven biped exhibits also such route to chaos when the slope angle is varied. For such biped, a modified semi-passive control law is introduced in order to stabilize the torso at some desired position. In this work, we will show through bifurcation diagrams that the dynamic walking of the two biped robots reveals two other routes to chaos namely the intermittency route and the interior crisis route. We will stress that the intermittency is generated via a saddle-node bifurcation where an unstable periodic orbit is created. We will highlight that such event takes place for a Type-I intermittency. However, we will emphasize that the interior crisis event occurs when a collision of the unstable periodic orbit with a weak chaotic attractor happens giving rise to a strong chaotic attractor. In addition, we will explore the intermittent step series induced by the interior crisis and also by the Type-I intermittency. In this study, our analysis on chaos and the routes to chaos will be based, beside bifurcation diagrams, on Lyapunov exponents and fractal (Lyapunov) dimension. These two tools are plotted in the parameter space to classify attractors observed in bifurcation diagrams.

Landscape ecology, land-use structure, and population density: Case study of the Columbus Metropolitan Area

Traditional population density models based on the distance to the major Central Business District (monocentric) or on distances to multiple employment centers (polycentric) are extended to include land-use structure variables derived from landscape ecology theory. A comprehensive database is developed for the Columbus Metropolitan Area (CMA) at the Traffic Analysis Zone (TAZ) level, using remotely sensed land-use data, Census socio-economic data, and other local data. Fifteen landscape indices, organized into four groups – size, complexity, diversity, neighborhood – are computed for each of the 1763 CMA TAZs, using Fragstats. Models are estimated for each of the 7 CMA counties separately, yielding homogeneous and consistent results. These county models are then pooled into a comprehensive CMA model, with dummy variables and second-order terms. Overall, the results provide evidence of a polycentric structure, with both downtown Columbus and county CBDs acting as strong population attractors, and of the importance of land-use structure in the determination of population density. Spatial indices representing neighborhood and diversity factors significantly impact population density in most counties.

Strong Uniform Attractors for Nonautonomous Suspension Bridge‐Type Equations

We discuss long‐term dynamical behavior of the solutions for the nonautonomous suspension bridge‐type equation in the strong Hilbert space , where the nonlinearity g(u, t) is translation compact and the time‐dependent external forces h(x, t) only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge‐type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.

Smooth Morse–Lyapunov Functions of Strong Attractors for Differential Inclusions

This paper is concerned with a smooth converse Lyapunov theorem for Morse decompositions of strong attractors of differential inclusion $x'(t)\in F(x(t))$, where $F$ is an upper semicontinuous multivalued mapping on $\mathbb{R}^m$ with compact convex values. Roughly speaking, let there be given a strong attractor $\mathscr{A}$ of the system with attraction basin $\Omega$ and Morse decomposition $\mathcal{M}=\{M_1,\ldots,M_l\}$. We will construct a radially unbounded function $V\in C^\infty(\Omega)$ such that (1) $V$ is constant on each Morse set $M_k$ and (2) $V$ is strictly decreasing along any solution of the system in $\Omega$ outside the Morse sets.

Strong Global Attractors for 3D Wave Equations with Weakly Damping

We consider the existence of the global attractor 𝒜1 for the 3D weakly damped wave equation. We prove that 𝒜1 is compact in and attracts all bounded subsets of with respect to the norm of . Furthermore, this attractor coincides with the global attractor in the weak energy space .

Academic careers for graduate students: a strong attractor in a changed environment

Professorship has traditionally been the single most valued career path for graduates of PhD programs. Policies now encourage graduate students to directly or indirectly engage with non-academic organizations to encourage the next generation of researchers to explore alternative careers, including opportunities in industry and government. In this article, we use data from a survey of Quebec science and engineering graduate students to examine the impact of their participation in university-industry-government research partnerships on their professional preferences. We assess the degree to which exposure to non-academic realities through different training arrangements relates to career preferences, and how these preferences evolve over time. We show that the proportion of students who did not change their preferred career path over time is high, indicating that by the time students engage in a research-training program they already, for the most part, know what career they want to pursue. However, and although students with close ties to non-academic partners may initially be more interested in non-academic career paths, over time all categories of students become more attracted to academic careers. We conclude that faculty positions continue to dominate the professional dreams of fledgling researchers, a power of attraction that increases as students advance in their program, even when it involves industrial contacts.

Strong trajectory attractors for dissipative Euler equations

The 2D Euler equations with periodic boundary conditions and extra linear dissipative term Ru, R > 0 are considered and the existence of a strong trajectory attractor in the space L loc ∞ ( R + , H 1 ) is established under the assumption that the external forces have bounded vorticity. This result is obtained by proving that any solution belonging the proper weak trajectory attractor has a bounded vorticity which implies its uniqueness (due to the Yudovich theorem) and allows to verify the validity of the energy equality on the weak attractor. The convergence to the attractor in the strong topology is then proved via the energy method.