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This article concerns an approximate solution for the Benjamin-Bona-Mahony (BBM) equation with a bilinear control in slowly varying medium. By a sharp estimation of the error term, a suitable approximate solution for this equation is established. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V, K, a, and f, we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case. [ABSTRACT FROM AUTHOR]

We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM) equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H¹ (ℝ) energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution. [ABSTRACT FROM AUTHOR]

In this paper we build a ternary-tree real options investment decision model of Integrated Gasification Combined Cycle (IGCC) power plant's Carbon Capture and Storage(CCS) project based on the real options model and establish three key factors influencing the CCS project: CCS technical progresses, feed-in tariff and carbon permit trading. Effects of these factors on CCS are considered. Through a scenario analysis of CCS project investment decision with given parameters, the effects of fluctuation of these three key factors-variation coefficient of feed-in tariffs, coal fuel prices and CERs(Certified Emission Reduction) on CCS investment decision are further analyzed which indicates that this model can be applied to investment decisions of CCS. [ABSTRACT FROM AUTHOR]

In real world, most systems show significant clustering, and it is more practical to investigate the behaviors of clustered network. Previous studies are mostly focused on single clustered network and coupled clustered networks with dependency links. Here we study two clustered networks coupled with both interdependent and interconnected links by introducing generating function of the joint degree distribution. When the networks are fully dependent, we obtain the analytical solution of giant component P∞. We show rich phase transition phenomena and analyze their behaviors. We find that, as dependency coupling strength increases, the system changes from second order phase transition through hybrid transition to first order phase transition. For weak dependency coupling strength qA, corresponding to second order phase transition, we find that, clustering has almost no effect on the robustness of network, but for strong dependency coupling strength qA, corresponding to first order transition, the more clustered system is more vulnerable. At the same time, we notice that when the system is more clustered, the hybrid order region is almost unchangeable, the first order region becomes smaller, and the second order region is larger. Additionally, we can see that, the bigger the clustering coefficient c is, the bigger the second order region becomes. For the same c, the density of connectivity links between networks is higher, the second order region becomes smaller, and the density of connectivity links within each network is higher, the second order region becomes bigger. [ABSTRACT FROM AUTHOR]

We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions. First we prove a local in time existence theorem and present a weak-strong uniqueness result. Then, we establish a asymptotic stabilization of this system by a boundary feedback. Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles. [ABSTRACT FROM AUTHOR]

This paper studies the wave-breaking criterion for the generalized weakly dissipative two-component Hunter-Saxton system in the periodic setting. We get local well-posedness for the generalized weakly dissipative two-component Hunter-Saxton system. We study a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globally L2 stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed. [ABSTRACT FROM AUTHOR]

We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3, 2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the modified Camassa–Holm equation is Painlevé integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation. [ABSTRACT FROM AUTHOR]

The Dullin–Gottwald–Holm equation can be described as the unidirectional propagation of surface waves in a shallow water regime. In this paper, we study the orbital stability problem of the peaked solitons (peakons) for the periodic Dullin–Gottwald–Holm equation on the line. By constructing a function only depending on three important conservative laws, we prove that the shapes of peakons are stable under small perturbations. We also demonstrate that the solutions of the Cauchy problem for this equation converge to those of the corresponding periodic Camassa–Holm equation as the linear dispersive parameter converges to zero. [ABSTRACT FROM AUTHOR]

We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbitrary-order nonlinearity. [ABSTRACT FROM AUTHOR]

This paper studies low-regularity solutions of the periodic Fornberg–Whitham equation with initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic Fornberg–Whitham equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation. We prove the global existence and uniqueness of solution to the viscous Degasperis–Procesi equation for u0∈L2(R). The local well posedness for u0∈L2(R) has been proven based on the energy estimate. The strong and weak limit behaviors of solution to the viscous Degasperis–Procesi equation are obtained. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the oligopoly model of nonrenewable resource in which the unit production cost is variable and depends on the resource reserve level. We consider both the open-loop strategy and the closed-loop strategy of this dynamical differential game. For the case of linear cost function we have observed that the open-loop equilibrium and the self-feedback equilibrium satisfy the same equilibrium conditions, which can be described as a dynamical system. The analysis shows that the equilibrium path of the model is the stable orbit of this system, and this result leads to further studies of the properties of the total extraction and reserve and the individual ones of each producer. For the total extraction rate and reserve, some of the properties are similar to those of most oligopoly models with fixed unit production cost. For the individual behaviors, we have found out the solution expressions of the individual extraction rate and resource reserve and got the main result that the producer with larger initial stock has a larger but declining market share and the share of each producer converges toward the average one when time approaches to infinite. [Copyright &y& Elsevier]

This paper studies the problem for optimal control of the viscous Degasperis-Procesi equation. The existence and uniqueness of weak solution to the equation are proved in a short interval. The optimal control of the viscous Degasperis-Procesi equation under boundary condition is given and the existence of optimal solution to the equation is proved. [ABSTRACT FROM AUTHOR]

In the paper what is studied is the wild solution of the induced form under the spline wavelet basis in weakly damped forced KdV equation. [ABSTRACT FROM AUTHOR]

When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here, we develop a mathematical framework and study numerically and analytically the percolation of interacting networks with feedback-dependency links. For the case that all degree distributions of intra- and inter- connectivity links are Poissonian, we find that for a low density of inter-connectivity links, the system undergoes from second order to first order through hybrid phase transition as coupling strength increases. It implies that the average degree k of inter-connectivity links has a little influence on robustness of the system with a weak coupling strength, which corresponds to the second order transition, but for a strong coupling strength corresponds to the first order transition. That is to say, the system becomes robust as k increases. However, as the average degree k of each network increases, the system becomes robust for any coupling strength. In addition, we find that one can take less cost to design robust system as coupling strength decreases by analyzing minimum average degree kmin of maintaining system stability. Moreover, for high density of inter-connectivity links, we find that the hybrid phase transition region disappears, the first order region becomes larger and second order region becomes smaller. For the case of two coupled scale-free networks, the system also undergoes from second order to first order through hybrid transition as the coupling strength increases. We find that for a weak coupling strength, which corresponds to the second order transitions, feedback dependency links have no effect on robustness of system relative to no-feedback condition, but for strong coupling strength which corresponds to first order or hybrid phase transition, the system is more vulnerable under feedback condition comparing with no-feedback condition. Thus, for designing resilient system, designers should try to avoid the feedback dependency links, because the existence of feedback- dependency links makes the system extremely vulnerable and difficult to defend. [ABSTRACT FROM AUTHOR]

The dynamics of the nonlinear Schördinger equation with Kerr law nonlinearity with two perturbation terms are investigated. By Using Melnikov method, the threshold values of chaotic motion under periodic perturbation are given .Moreover we also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, chaos threshold diagram of system in three-dimensional space, maximum Lyapunov exponent, and phase portraits, are also plotted to illustrate theoretical analysis and to expose the complex dynamical behaviors. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting controller e, amplitude d 1, and frequency ω2of external forcing which can be considered a control strategy, and when the frequencies y ω2 and ω1 approach the maximum frequency of disturbance, the system turmoil intensifies and control intensity increases. [ABSTRACT FROM AUTHOR]

In underwater acoustic sensor networks (UASNs), the propagation delay of acoustic signals is much longer than Radio Frequency (RF). There is spatial unfairness problem caused by space-time uncertainty. Hence, the design of Medium Access Control (MAC) is a challenging issue. In underwater, it not only considers transmission time but also takes location into account. In this paper, we propose Response to the Earliest Transmitter of RTS MAC (RET-MAC) protocol to solve the problem. RET-MAC adopts adaptive RTS Contention Phase (RTS CP) to determine the earliest transmitter of RTS. And CTS Delay Phase (CTS DP) is added to postpone sending CTS in order to avoid collision. In addition, we propose CTS back-off mechanism to adjust the length of CTS DP as needed. Contention back-off mechanism is used to reduce network congestion and increase fairness further. The simulation results show that our scheme can achieve higher fairness and throughput; at the same time it also guarantees lower energy consumption and delay. [ABSTRACT FROM AUTHOR]

We study a system composed of two partially interdependent networks; when nodes in one network fail, they cause dependent nodes in the other network to also fail. In this paper, the percolation of partially interdependent networks under targeted attack is analyzed. We apply a general technique that maps a targeted-attack problem in interdependent networks to a random-attack problem in a transformed pair of interdependent networks. We illustrate our analytical solutions for two examples: (i) the probability for each node to fail is proportional to its degree, and (ii) each node has the same probability to fail in the initial time. We find the following: (i) For any targeted-attack problem, for the case of weak coupling, the system shows a second order phase transition, and for the strong coupling, the system shows a first order phase transition, (ii) For any coupling strength, when the high degree nodes have higher probability to fail, the system becomes more vulnerable, (iii) There exists a critical coupling strength, and when the coupling strength is greater than the critical coupling strength, the system shows a first order transition; otherwise, the system shows a second order transition. [ABSTRACT FROM AUTHOR]

Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic-paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields. [ABSTRACT FROM AUTHOR]

As a developing country, extensive carbon and sulfur emissions are associated with China’s rapid social and economic development. Chief among them are the emissions from coal and oil consumption. This paper focuses on the demand side, attempting to regulate the range of relative price of oil to coal at the consumption level. Through the adjustment of the relative price, the goal of reducing the emissions of carbon and sulfur could be achieved in the market of energy consumption. Data regression is applied to investigate the functional relationship between emissions and energy prices. The results indicate that when the coal price is less than 300, the higher relative price leads to less carbon and sulfur emissions; when the coal price is more than 300 and less than 500, there exists an optimal relative price which has the least carbon emissions, and this value is not more than 11.5; when the coal price is more than 500, the smaller relative price is beneficial to decline carbon and sulfur emissions. The changed trend of relative price-sulfur emissions is very similar to relative price-carbon emissions. Compared to the present energy situation in China, the relative price of oil to coal still need to be reduced especially when coal price is more than 500. [ABSTRACT FROM AUTHOR]

The thermal stability of the standard Ni/SiC and a TiW/Ni/SiC Ohmic contacts was investigated and compared after being aged at 400 °C in the 2N2 atmosphere. The Ohmic contact was characterized using a combination of I-V measurements, the optical microscopic imaging, X-ray diffraction (XRD), and Auger electron spectroscopy (AES) techniques. It is shown that the standard Ni/SiC Ohmic contact failed after being aged at 400 °C for 20 h in the N2 atmosphere, while the TiW/Ni/SiC Ohmic contact could stand after 100 h. The TiW/Ni/SiC Ohmic contact was found kept a smooth surface morphology during the rapid thermal annealing and aging process, while the standard Ni/SiC Ohmic metal surface was found rougher. Both the Ohmic contact deteriorations after high temperature aging could be attributed to the formation of graphite which is confirmed by the XRD results. The XRD and AES results reveal that the better thermal stability of the TiW/Ni/SiC could be explained by the formation of CW3 and TiC, which deter the C atom diffusion to form graphite. [ABSTRACT FROM AUTHOR]

We report a new method for growing hexagonal columnar nanograin structured silicon carbide (SiC) thin films on silicon substrates by using graphene-graphitic carbon nanoflakes (GGNs) templates from solid carbon sources. The growth was carried out in a conventional low pressure chemical vapor deposition system (LPCVD). The GGNs are small plates with lateral sizes of around 100 nm and overlap each other, and are made up of nanosized multilayer graphene and graphitic carbon matrix (GCM). Long and straight SiC nanograins with hexagonal shapes, and with lateral sizes of around 200-400 nm are synthesized on the GGNs, which form compact SiC thin films. [ABSTRACT FROM AUTHOR]

Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős–Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value qc. Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q < qc, the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA. [ABSTRACT FROM AUTHOR]

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms. [ABSTRACT FROM AUTHOR]