The complexity of advice‐giving

Advice‐giving about personal problems is a common form of human interaction. However, an open question is whether there is an abstract and general logic that explains how advice‐giving works. In this study, we addressed this question from the perspective of dynamical systems. We measured the nonlinear dynamics of advice‐giving by using recurrence quantification analysis. Analyzing 600 texts of request for advice and the advice given, our results uncover a typical logic of advice‐giving, and suggest that advice‐giving may be understood as a dynamic manipulation of perspective‐taking. © 2009 Wiley Periodicals, Inc. Complexity 2009     

Singular perturbations and vanishing passage through a turning point

The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics can be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer variable still is. We provide general results as well as a number of applications. We show how to treat the open problems presented in Artés et al. (2009) [1] and Dumortier and Rousseau (2009) [13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) [14].     

Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Using the weak asymptotic method, we approximate a triangular system of conservation laws arising from the so‐called generalized pressureless gas dynamics by a diagonal linear system. Then, we apply the usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how the delta shock wave naturally arises along the characteristics. Also, we propose a procedure that could be applied to more general systems of conservation laws. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation

We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells.     

The dynamics of a Bertrand duopoly with differentiated products: Synchronization,intermittency and global dynamics

We study the dynamics of a duopoly game à la Bertrand with horizontal product differentiation as proposed by Zhang et al. (2009) [35] by introducing opportune microeconomic foundations. The final model is described by a two-dimensional non-invertible discrete time dynamic system T. We show that synchronized dynamics occurs along the invariant diagonal being T symmetric; furthermore, we show that when considering the transverse stability, intermittency phenomena are exhibited. In addition, we discuss the transition from simple dynamics to complex dynamics and describe the structure of the attractor by using the critical lines technique. We also explain the global bifurcations causing a fractalization in the basin of attraction. Our results aim at demonstrating that an increase in either the degree of substitutability or complementarity between products of different varieties is a source of complexity in a duopoly with price competition.     

Modeling dynamics of an influenza pandemic with heterogeneous coping behaviors: case study of a 2009 H1N1 outbreak in Arizona

This paper aims to improve the accuracy of standard compartment models in modeling the dynamics of an influenza pandemic. Standard compartment models, which are commonly used in influenza simulations, make unrealistic assumptions about human behavioral responses during a pandemic outbreak. Existing simulation models with public avoidance also make a rigid assumption regarding the human behavioral response to influenza. This paper incorporates realistic assumptions regarding individuals’ avoidance behaviors in a standard compartment model. Both the standard and modified models are parameterized, implemented, and compared in the research context of the 2009 H1N1 influenza outbreak in Arizona. The modified model with heterogeneous coping behaviors forecasts influenza spread dynamics better than the standard model when evaluated against the empirical data, especially for the beginning of the 2009–2010 normal influenza season starting in October 2009 (i.e., the beginning of the second wave of 2009 H1N1). We end the paper with a discussion of the use of simulation models in efforts to help communities effectively prepare for and respond to influenza pandemics.     

Permanence and global stability of a class of discrete epidemic models

In this paper we investigate the permanence of a system and give a sufficient condition for the endemic equilibrium to be globally asymptotically stable, which are the remaining problems in our previous paper (G. Izzo, Y. Muroya, A. Vecchio, A general discrete time model of population dynamics in the presence of an infection, Discrete Dyn. Nat. Soc. (2009), Article ID 143019, 15 pages. doi:10.1155/2009/143019.)     

Quantum trajectories of an oscillator interacting with an electromagnetic field, a classical force, and a heat bath

We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field, a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009.     

Strong stabilization of a structural acoustic model,which incorporates shear and thermal effects in the structural component

In this paper we consider the question of stabilization of a linear three‐dimensional structural acoustic model, which incorporates displacement, rotational inertia, shear and thermal effects in the flat flexible structural component of the model. We show strong stabilization of the coupled model without incorporating viscous or boundary damping in the equations for the gas dynamics and without imposing geometric conditions. It turns out that damping is needed in the interior of the plate. Our main tool is an abstract resolvent criterion due to Y. Tomilov. Copyright © 2009 John Wiley & Sons, Ltd.     

Competitive carbon emission yields the possibility of global self-control

Despite many international climate meetings such as Copenhagen 2009, it is still unclear how annual global emissions can be reduced without requiring governments to micro-manage the emitting companies within their individual jurisdictions. Here we examine a simple, yet highly non-trivial, computer model of carbon emission which is consistent with recent activity in the European carbon markets. Our simulation results show that the ongoing daily competition to emit CO₂ within a population of emitters, can lead to a form of collective self-control over the aggregated emissions. We identify regimes in which such a population spontaneously hits its emissions target with minimal fluctuations. We then focus on the emission dynamics induced by a governing body which chooses to actively manage the capping level. Finally we lay some formal stepping stones toward a complete analytic theory for carbon emissions fluctuations within this model framework – in so doing, we also connect this problem to more familiar theoretical terrain within computer science.     

Two‐soliton solutions to the three‐dimensional gravitational Hartree equation

We construct nondispersive two‐soliton solutions to the three‐dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the gravitational two‐body problem. © 2009 Wiley Periodicals, Inc.     

Constructive effects of diversity in a multi-neuron model of the homeostatic regulation of the sleep–wake cycle

As an instance of diversity-induced resonance and of the constructive role of heterogeneity in complex systems, here we study a generalized version of a physiologically-motivated sleep–wake cycle model taking into account the role of orexin [Patriarca et al. (2012) [16]; Postnova et al. (2009) [9]]. With respect to the versions of the model studied previously, here we consider systems containing both a set of orexin neurons — responsible for the production of orexin — and a set of glutaminergic neurons — representing mental activity or sleep depending on their firing or silent state, respectively — within some basic network topologies. The neurons of one or both types are diversified and it is shown how the interplay between the heterogeneous constituent units produces as an emergent effect the recovering or improving of the sleep-wake cycle. At a general level, the results obtained suggest that also systems with a dynamics driven by a homeostatic mechanism, with a time scale much longer than that of the constituent excitable units, may present diversity-induced resonance.     

A Comparison of Alternative Space-Time Discretizations of Nonlinear Shells

Geometrically exact shell models are suitable for modelling shell-type flexible components in the context of finite-deformation multibody dynamics. Conserving time-stepping schemes are known to yield enhanced numerical stability properties. This approach is compared to alternative methods, including a momentum-symplectic variational integrator. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The numerical simulation of a typical fluid-structure interaction problem

To determine the dynamic response of a structure under the influence of the fluid flow one must solve a coupled computational fluid dynamics (CFD) and computational structural dynamics (CSD) mathematical problem. This paper presents the comparison of two methods for the calculation of the fluid-structure interaction. The first one is of explicit-implicit type and uses a staggered time advancement of the fluid and structure problems. The second uses a fully implicit discretization in the physical time of the fluid-structure equations and an explicit advancement in the dual-time. The physical fluid-structure problem is accompanied by the equations of the mesh motion, which are written as for a pseudo-structural system with its own dynamics. Representative numerical results are presented for the two degrees of freedom tipical section in unsteady transonic flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient inviscid flow in a passive linear model of the cochlea

Detailed knowledge of the fluid dynamics within the cochlea is important for a complete understanding of the physiology of this complex organ. We present a numerical simulation in the time domain for the inviscid two-dimensional flow in a passive cochlea. Numerical results are presented for a click stimulation and an impulsively started tone. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Qualitative and quantitative combined nonlinear dynamics model and its application in analysis of price,supply–demand ratio and selling rate

The qualitative and quantitative combined nonlinear dynamics model proposed in this paper fill the gap in nonlinear dynamics model in terms of qualitative and quantitative combined methods, allowing the qualitative model and quantitative model to perfectly combine and overcome their weaknesses by learning from each other. These two types of models use their strengths to make up for the other’s deficiencies. The qualitative and quantitative combined models can surmount the weakness that the qualitative model cannot be applied and verified in a quantitative manner, and the high costs and long time of multiple construction as well as verification of the quantitative model. The combined model is more practical and efficient, which is of great significance for nonlinear dynamics. The qualitative and quantitative combined modeling and model analytical method raised in this paper is not only applied to nonlinear dynamics, but can be adopted and drawn on in the modeling and model analysis of other fields. Additionally, the analytical method of qualitative and quantitative combined nonlinear dynamics model proposed in this paper can satisfactorily resolve the problems with the price system’s existing nonlinear dynamics model analytical method. The three-dimensional dynamics model of price, supply–demand ratio and selling rate established in this paper make estimates about the best commodity prices using the model results, thereby providing a theoretical basis for the government’s macro-control of price. Meanwhile, this model also offer theoretical guidance to how to enhance people’s purchasing power and consumption levels through price regulation and hence to improve people’s living standards.     

Complex dynamic behavior during transition in a solid combustion model

Through examples in a free‐boundary model of solid combustion, this study concerns nonlinear transition behavior of small disturbances of front propagation and temperature as they evolve in time. This includes complex dynamics of period doubling, and quadrupling, and it eventually leads to chaotic oscillations. Within this complex dynamic domain we also observe a period six‐folding. Both asymptotic and numerical solutions are studied.We show that for special parameters our asymptotic method with some dominant modes captures the formation of coherent structures. Finally,we discuss possible methods to improve our prediction of the solutions in the chaotic case. © 2009 Wiley Periodicals, Inc. Complexity, 2009