扰动mKdV耦合系统的孤子解

采用了一个简单而有效的技巧,研究了一类扰动mKdV耦合系统.首先利用同伦映射方法求解一个相应的复值函数微分方程孤子的近似解.然后得到了原扰动mKdV耦合系统孤子的近似解. 关键词： 孤子 扰动mKdV方程 同伦映射     

A numerical algorithm for pricing electricity derivatives for jump-diffusion processes based on continuous time lattices

We present a numerical algorithm for pricing derivatives on electricity prices. The algorithm is based on approximating the generator of the underlying price process on a lattice of prices, resulting in an approximation of the stochastic process by a continuous time Markov chain. We numerically study the rate of convergence of the algorithm for the case of the Merton jump-diffusion model and apply the algorithm to calculate prices and sensitivities of both European and Bermudan electricity derivatives when the underlying price follows a stochastic process which exhibits both fast mean-reversion and jumps of large magnitude.     

Evolutionary games with facilitators: When does selection favor cooperation?

We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy (“cooperation” and “defection”) games in populations comprising cooperation facilitators. The latter are individuals that support cooperation by enhancing the reproductive potential of cooperators relative to the fitness of defectors. By computing the fixation probability of a single cooperator in finite and well-mixed populations that include a fixed number of facilitators, and by using mean field analysis, we determine when selection promotes cooperation in the important classes of prisoner’s dilemma, snowdrift and stag-hunt games. In particular, we identify the circumstances under which selection favors the replacement and invasion of defection by cooperation. Our findings, corroborated by stochastic simulations, show that the spread of cooperation can be promoted through various scenarios when the density of facilitators exceeds a critical value whose dependence on the population size and selection strength is analyzed. We also determine under which conditions cooperation is more likely to replace defection than vice versa.     

Global synchronization of weighted cellular neural network with time-varying coupling delays

New sufficient conditions are derived to guarantee the global synchronization of the weighted cellular neural network with multiple time delays. Based on Lyapunov theory, this paper proposes an adaptive feedback controlling method to identify the exact topology of a rather general weighted cellular neural network system with time-varying delays and then considers the synchronization of the neural network with different nodes dynamics. The parameters in this paper are very few and experiments show that the methods presented in this paper are of high application in global synchronization.     

Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators

In this work, a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators is investigated. By the stroboscopic map of the discrete dynamical system, the prey-extinction periodic solution of the investigated system is proved to be globally asymptotically stable. By the theory of impulsive differential equation, the investigated system is also proved to be permanent. Finally, the numerical analysis is inserted to illustrate the results. Our conclusions provide reliable tactical basis for the practical biological management.     

Fractional dynamics of a system with particles subjected to impacts

This paper studies the dynamics of a system composed of a collection of particles that exhibit collisions between them. Several entropy measures and different impact conditions of the particles are tested. The results reveal a Power Law evolution both of the system energy and the entropy measures, typical in systems having fractional dynamics.     

Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms

Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order linearizable ODEs and then applying the Ibragimov and Meleshko linearization test for the obtained ODEs. The application of the algorithm to several ODEs is also presented.     

Pricing range notes within Wishart affine models

We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and a dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.     

Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model

This paper considers an asset-liability management (ALM) problem under a continuous-time Markov regime-switching model. By adopting the techniques of [Zhou, X.Y., Yin, G., 2003. Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM J. Control Optim. 42, 1466–1482], we investigate the feasibility, obtain the optimal strategy, delineate the efficient frontier, and establish the associated mutual fund theorem.     

Average Range and Network Synchronizability

The influence of structural properties of a network on the network synchronizability is studied by introducing a new concept of average range of edges. For both small-world and scale-free networks, the effect of average range on the synchronizability of networks with bounded or unbounded synchronization regions is illustrated through numerical simulations. The relations between average range, range distribution, average distance, and maximum betweenness are also explored, revealing the effects of these factors on the network synchronizability of the small-world and scale-free networks, respectively.