Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 2016"

TL;DR: The results are derived under suitable assumptions for the current velocity associated with corresponding boundary conditions of the fluid density, and under corresponding parametric constraints.

TL;DR: It is demonstrated that the modified Riemann–Liouville fractional derivatives cannot be considered as derivatives of non-integer order if the suggested chain rule holds.

TL;DR: A new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order, and for each one of them an approximation formula is obtained in terms of standard (integer-order) derivatives only.

TL;DR: The results of multi-parameter management analysis may give theoretical support as well as further impetus in the experimental investigation on soliton excitations, elastic and inelastic collisions in alpha helical proteins with interspine coupling at higher order.

TL;DR: A fast and accurate method for numerical solutions of space fractional reaction–diffusion equations based on an exponential integrator scheme in time and the Fourier spectral method in space, which yields a fully diagonal representation of the fractional operator with increased accuracy and efficiency.

TL;DR: It is found that fluctuations in population levels arising due to gestation delay of predator can be prevented under certain parametric conditions and increasing delays may cause bifurcations into periodic solutions.

TL;DR: Fractal time and space derivatives into Fick's second law of diffusion provide a more natural way to link sub-voxel tissue composition with the observed diffusion signal decay following the application of a diffusion-sensitive pulse sequence.

TL;DR: The reduced dynamics associated with Turing–Hopf bifurcation is exactly the dynamics of codimension–two ordinary differential equations (ODE), which implies the ODE techniques can be employed to classify the reduced dynamics by the unfolding parameters.

TL;DR: The proposed mathematical representation can be useful to understand electrochemical phenomena, propagation of energy in dissipative systems, irreversible thermodynamics, quantum optics or turbulent diffusion, thermal stresses, models of porous electrodes, the description of gel solvents and anomalous complex processes.

TL;DR: In general, the performance of car-following model can be improved with an exterior control method and with the increasing compensation parameters the stability of the car- following system is strengthened.

TL;DR: Based on the dynamical behavior of solution, the classification of the localized wave solutions on the nonzero background is given explicitly and the parameter conditions for breather, dark soliton and rogue wave solution of mCNLSE are given in detail.

TL;DR: It is shown that an implicit difference scheme is proposed, under the assumption that the analytical solution decays to zero when the space variable x tends to infinity, that conserves the mass and energy and is unconditionally stable with respect to the initial values.

TL;DR: This paper aims to discuss the logistic equation subject to uncertainties in two parameters: the environmental carrying capacity, K, and the initial population density, N 0, and provides closed-form results for the first probability density function of time-population density.

TL;DR: By using an impulsive integral inequality, some novel sufficient conditions are derived to ensure the exponential stability of mild solution in the mean square moment of impulsive neutral stochastic integrodifferential equations driven by a fractional Brownian motion.

TL;DR: A new car-following model is constructed by accounting for the effect of the optimal velocity changes with memory in terms of the full velocity difference (FVD) model and it is shown that the effect could enhance the stability of traffic flow.

TL;DR: It can be found that the improved car-following model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that taking relative velocity fluctuation into account in designing the advanced adaptive cruise control strategy can improve the traffic flow stability and reduce fuel consumptions.

TL;DR: The generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations are compared and the results might be useful for the signal processing of nonlinear systems.

TL;DR: It is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which satisfy the classical physical limitations.

TL;DR: This work introduces new integral and differential operators for the description of Havriliak–Negami models in the time-domain and proposes a formulation of Grunwald–Letnikov type which turns out to be effective not only to provide a theoretical characterization of the operators associated to HavRiliak-Negami systems but also for computational purposes.

TL;DR: In this article, the authors investigated stability and asymptotic properties of autonomous fractional differential systems with a time delay and derived necessary and sufficient stability conditions via eigenvalues of the system matrix and their location in a specific area of the complex plane.

TL;DR: A stochastic phytoplankton allelopathy model, which takes both white and colored noises into account, is developed and analyzed, which proves the existence of the global positive solution of the model and investigates the positive recurrence and ergodic property of the models.

TL;DR: It is reported that there are possibilities to ‘catch’ rogue waves through manipulating nonlinear function and gain/loss coefficient.

TL;DR: Theoretically, the asymptotic stability of the malware-free equilibrium is confirmed when the threshold is below the unity, and the global stability is further proved under some sufficient conditions.

TL;DR: A systematic analysis of a system consisting of an autonomous third order Duffing–Holmes type chaotic oscillator, where some regions of the parameter space corresponding to the coexistence of multiple attractors are discovered, represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general.

TL;DR: It is revealed that a special kind of Poisson stable point, which the authors call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set.

TL;DR: In terms of bifurcation diagrams and phase portraits, the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.

TL;DR: A novel adaptive control law is designed, from which the two problems, i.e., parameter estimation and reference tracking, can be unified perfectly, and an effective control scheme is established.

TL;DR: In this paper, an improved Cattaneo-Christov flux model is proposed to capture the effects of the time and spatial relaxations, the time-and spatial inhomogeneous diffusion and the spatial transition probability of cell transport in a highly non-homogeneous medium.

TL;DR: A new dual channel transmission mechanism is presented and used in secure communication scheme design, then the channel-switching techniques are adopted to further improve the security of information transmission.

TL;DR: A modified CH equation with an interfacial profile correction term is proposed, which greatly simplifies gridding, discretization, and handling of topological changes in a phase-field fluid model and computation with minimized Cahn–Hilliard dynamics.