Narrow Results

We construct examples of vector fields on a three-sphere, amenable to analytic proof of properties that guarantee the existence of complex behavior. The examples are restrictions of symmetric polynomial vector fields in R⁴ and possess heteroclinic networks producing switching and nearby suspended horseshoes. The heteroclinic networks in our examples are persistent under symmetry preserving perturbations. We prove that some of the connections in the networks are the transverse intersection of invariant manifolds. The remaining connections are symmetry-induced. The networks lie in an invariant three-sphere and may involve connections exclusively between equilibria or between equilibria and periodic trajectories. The same construction technique may be applied to obtain other examples with similar features.

In this paper we discuss the practical usefulness of nonlinear dynamical analysis for the design of a planar cable-supported beam: we refer to a feasible case, assuming the value of the parameters corresponding to a realistic pedestrian footbridge. We consider a one degree of freedom model, obtained by the classical Galerkin reduction technique: the ensuing ordinary differential equation has both quadratic and cubic terms, due to geometric nonlinearities. Extensive numerical simulations are performed: they point out that this model, in spite of its apparent simplicity, is able to highlight the complex dynamics of the cable-supported beam, describing several common and uncommon nonlinear phenomena. Each of them is interpreted in terms of oscillations of the considered mechanical system; we explain the relevance of all the obtained results in the design of the examined structure under steady loads as wind and pedestrians, but also under transient phenomena as earthquake and gust; the ensuing issues, the most dangerous ranges and also the sensibility to perturbations are discussed in detail. In particular we deal with the importance, for an engineering design, of a careful interpretation of: isola bifurcation, transition to chaos both by period doubling cascade and reverse boundary crisis, multistability with coexistence of chaotic and periodic attractors, fractal basins boundaries, erosion of immediate basins, interrupted sequence of period doubling bifurcations. Also the effects of secondary attractors are analyzed, and it is shown that in general they cannot be neglected even if their range of existence is very small. We underline that all these investigations are performed choosing the excitation frequency far from resonances in order to alert the designer that the system dynamics may be complex independently of the activation mechanism due to resonance.

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, RSA algorithm, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking.

Deflection routing is a mechanism to route packets away from congestion. Traditional shortest path routing uses only the static topological information as input, whereas deflection routing takes into account the dynamic queue length information. In the simplest form of deflection routing, a packet being dropped due to queue buffer overflow is "rescued" and is rerouted to other links. Deflection routing can thus reduce the rate of packet drops and allow a network to carry more packets without the need of additional bandwidth. However, it can also lead to unstable deflecting behavior in some congestion scenario. It is important to study deflection behavior when operating near the point of congestion. In this paper, the performance in terms of packet drop rate and traveling time are studied through extensive simulation, and complex behavior in the traffic with self-similarity property is observed and discussed.

Motivated by the Silk Road Economic Belt and the 21st-Century Maritime Silk Road project, i.e. the Belt and Road (B&R), more goods will flow around the world. With this trading platform, people can buy products at relatively cheap prices, and it is easier for people to buy various goods. The quality and quantity of products thus attract more and more attention in the supply chains. This paper discusses the quantity decision by considering the product quality in parallel supply chains where two manufacturers produce substitute products and then sell them to their downstream retailers separately. In terms of the changing quantity, as well as the different quality, this paper establishes a dynamic game model to explore the dynamic behavior when the optimal profits of two retailers have been calculated. The dynamic behaviors of the system, such as stable region, bifurcation and chaos, strange attractors and the largest Lyapunov exponents (LLE) are analyzed. The effect of the quantity adjustment parameter on the stability of the supply chain system is investigated through numerical simulations. Furthermore, a dynamic game model is established based on the quality delay decision, to investigate the influence of the quality delay parameter on the dynamic game model and the profits. Finally, the optimal decisions are obtained and analyzed.

Multiagent systems (MAS) provide a useful tool for exploring the complex dynamics and behavior of financial markets and now MAS approach has been widely implemented and documented in the empirical literature. This paper introduces the implementation of an innovative multi-scale mathematical model for a computational agent-based financial market. The paper develops a method to quantify the degree of self-organization which emerges in the system and shows that the capacity of self-organization is maximized when the agent behaviors are heterogeneous. Numerical results are presented and analyzed, showing how the global market behavior emerges from specific individual behavior interactions.

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.