Ordered chaotic bursting and multiple coherence resonance by time-periodic coupling strength in Newman–Watts neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the temporal coherence of the chaotic bursting of Newman–Watts thermosensitive neuron networks. It is found that the chaotic bursting can exhibit coherence resonance and multiple coherence resonance behavior when TPCS amplitude and frequency is varied, respectively. It is also found that TPCS can also enhance the temporal coherence and spatial synchronization of the optimal spatio-temporal bursting in the case of fixed coupling strength. These results show that TPCS can tame the chaotic bursting and can repeatedly enhance the temporal coherence of the chaotic bursting neuronal networks. This implies that TPCS may play a more efficient role for improving the time precision of the information processing in chaotic bursting neurons.     

A multirate W-method for electrical networks in state–space formulation

Subunits of coupled technical systems typically behave on differing time scales, which are often separated by several orders of magnitude. An ordinary integration scheme is limited by the fastest changing component, whereas so-called multirate methods employ an inherent step size for each subsystem to exploit these settings. However, the realization of the coupling terms is crucial for any convergence. Thus the approach to return to one-step methods within the multirate concept is promising. This paper introduces the multirate W-method for ordinary differential equations and gives a theoretical discussion in the context of partitioned Rosenbrock–Wanner methods. Finally, the MATLAB implementation of an embedded scheme of order (3)2 is tested for a multirate version of Prothero–Robinson's equation and the inverter-chain-benchmark.     

Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise

Stochastic resonance is investigated to explain the beneficial effect of Lévy noise on gene expression of genetic toggle model with harmonic excitation. The dynamic change of protein concentration of genetic toggle model under combined drives of harmonic excitation and Lévy noise is obtained numerically. Stochastic resonance is presented through the classical measure of signal-to-noise-ratio. Then from two aspects of combined drives on the protein at high or low concentration, the changes of protein concentration and signal-to-noise-ratio are discussed, respectively. When combined drives are within the protein at high concentration, the increasing Lévy noise intensity can promote the transition between the high and low concentrations, and the low protein concentration hardly fluctuates under the small noise intensity. It is also shown that the increase of stability index, skewness parameter of Lévy noise and amplitude of harmonic excitation can suppress the optimum collaboration of stochastic resonance. On the other hand, when combined drives are within the protein at low concentration, the increasing noise intensity can enhance the transition between the high and low concentrations, and the increase of stability index, skewness parameter and amplitude can strengthen the optimum collaboration of stochastic resonance. By the synergic actions of stochastic resonance, it is demonstrated that combined effect of harmonic excitation and Lévy stimuli can be utilized to promote the gene expression of proteins in genetic toggle model.     

Stochastic exponential robust stability of interval neural networks with reaction–diffusion terms and mixed delays

The stochastic exponential robust stability is considered for a class of delayed neural networks with reaction–diffusion terms and Markov jumping parameters in this paper. It is assumed that the uncertain weight matrices belong to the given interval matrices. Some sufficient conditions for the stochastic exponential robust stability of the system are established by applying vector Lyapunov function method and M-matrix theory. The obtained results involving the effect of reaction–diffusion improve the existing conditions. Finally, two examples with numerical simulations are given to illustrate the obtained results.     

Parametric resonance in the Rayleigh–Duffing oscillator with time-delayed feedback

We investigate the principal parametric resonance of a Rayleigh–Duffing oscillator with time-delayed feedback position and linear velocity terms. Using the asymptotic perturbation method, we obtain two slow flow equations on the amplitude and phase of the oscillator. We study the effects of the frequency detuning, the deterministic amplitude, and the time-delay on the dynamical behaviors, such as stability and bifurcation associated with the principal parametric resonance. Moreover, the appropriate choice of the feedback gain and the time-delay is discussed from the viewpoint of vibration control. It is found that the appropriate choice of the time-delay can broaden the stable region of the non-trivial steady-state solutions and enhance the control performance. Theoretical stability analysis is verified through a numerical simulation.     

Optimal autaptic and synaptic delays enhanced synchronization transitions induced by each other in Newman–Watts neuronal networks

In this paper, we numerically study the effect of electrical autaptic and synaptic delays on synchronization transitions induced by each other in Newman–Watts Hodgkin–Huxley neuronal networks. It is found that the synchronization transitions induced by synaptic delay vary with varying autaptic delay and become strongest when autaptic delay is optimal. Similarly, the synchronization transitions induced by autaptic delay vary with varying synaptic delay and become strongest at optimal synaptic delay. Also, there is optimal coupling strength by which the synchronization transitions induced by either synaptic or autaptic delay become strongest. These results show that electrical autaptic and synaptic delays can enhance synchronization transitions induced by each other in the neuronal networks. This implies that electrical autaptic and synaptic delays can cooperate with each other and more efficiently regulate the synchrony state of the neuronal networks. These findings could find potential implications for the information transmission in neural systems.     

Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps

We consider jump-type stochastic differential equations with drift, diffusion, and jump terms. Logarithmic derivatives of densities for the solution process are studied, and Bismut–Elworthy–Li-type formulae are obtained under the uniformly elliptic condition on the coefficients of the diffusion and jump terms. Our approach is based upon the Kolmogorov backward equation by making full use of the Markov property of the process.     

Stochastic Lotka–Volterra systems with Lévy noise

This paper is concerned with stochastic Lotka–Volterra models perturbed by Lévy noise. Firstly, stochastic logistic models with Lévy noise are investigated. Sufficient and necessary conditions for stochastic permanence and extinction are obtained. Then three stochastic Lotka–Volterra models of two interacting species perturbed by Lévy noise (i.e., predator–prey system, competition system and cooperation system) are studied. For each system, sufficient and necessary conditions for persistence in the mean and extinction of each population are established. The results reveal that firstly, both persistence and extinction have close relationships with Lévy noise; Secondly, the interaction rates play very important roles in determining the persistence and extinction of the species.     

Stochastic predator–prey model with Allee effect on prey

We study a predator–prey model with the Allee effect on prey and whose dynamics is described by a system of stochastic differential equations assuming that environmental randomness is represented by noise terms affecting each population. More specifically, we consider a term that expresses the variability of the growth rate of both species due to external, unpredictable events. We assume that the intensities of these perturbations are proportional to the population size of each species. With this approach, we prove that the solutions of the system have sample pathwise uniqueness and bounded moments. Moreover, using an Euler–Maruyama-type numerical method we obtain approximated solutions of the system with different intensities for the random noise and parameters of the model. In the presence of a weak Allee effect, we show that long-term survival of both populations can occur. On the other hand, when a strong Allee effect is considered, we show that the random perturbations may induce the non-trivial attracting-type invariant objects to disappear, leading to the extinction of both species. Furthermore, we also find the Maximum Likelihood estimators for the parameters involved in the model.     

Stochastic Cahn–Hilliard equation with singular nonlinearity and reflection

We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space–time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical penalization method, which uses a crucial monotonicity property. Being inspired by the works of Debussche and Zambotti, we use a method based on infinite dimensional equations, approximation by regular equations and convergence of the approximated semigroup. We obtain existence and uniqueness of a solution for nonnegative initial conditions, results on the invariant measures, and on the reflection measures.     

Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market

This paper considers a non-self-financing mean-variance portfolio selection problem in which the stock price and the stochastic cash flow follow a Markov-modulated Lévy process and a Markov-modulated Brownian motion with drift, respectively. The stochastic cash flow can be explained as the stochastic income or liability of the investors during the investment process. The existence of optimal solutions is analyzed, and the optimal strategy and the efficient frontier are derived in closed-form by the Lagrange multiplier technique and the LQ (Linear Quadratic) technique.     

Euler–Maruyama Approximations for Stochastic McKean–Vlasov Equations with Non-Lipschitz Coefficients

Journal of Theoretical Probability - In this paper, we study a type of stochastic McKean–Vlasov equations with non-Lipschitz coefficients. Firstly, by an Euler–Maruyama approximation...     

Hub location–allocation in intermodal logistic networks

Within the context of intermodal logistics, the design of transportation networks becomes more complex than it is for single mode logistics. In an intermodal network, the respective modes are characterized by the transportation cost structure, modal connectivity, availability of transfer points and service time performance. These characteristics suggest the level of complexity involved in designing intermodal logistics networks. This research develops a mathematical model using the multiple-allocation p-hub median approach. The model encompasses the dynamics of individual modes of transportation through transportation costs, modal connectivity costs, and fixed location costs under service time requirements. A tabu search meta-heuristic is used to solve large size (100 node) problems. The solutions obtained using this meta-heuristic are compared with tight lower bounds developed using a Lagrangian relaxation approach. An experimental study evaluates the performance of the intermodal logistics networks and explores the effects and interactions of several factors on the design of intermodal hub networks subject to service time requirements.     

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.     

An Indefinite Stochastic Linear Quadratic Optimal Control Problem with Delay and Related Forward–Backward Stochastic Differential Equations

In this paper, we will study an indefinite stochastic linear quadratic optimal control problem, where the controlled system is described by a stochastic differential equation with delay. By introducing the relaxed compensator as a novel method, we obtain the well-posedness of this linear quadratic problem for indefinite case. And then, we discuss the uniqueness and existence of the solutions for a kind of anticipated forward–backward stochastic differential delayed equations. Based on this, we derive the solvability of the corresponding stochastic Hamiltonian systems, and give the explicit representation of the optimal control for the linear quadratic problem with delay in an open-loop form. The theoretical results are validated as well on the control problems of engineering and economics under indefinite condition.     

The uniqueness property for networks with several origin–destination pairs

We consider congestion games on networks with nonatomic users and user-specific costs. We are interested in the uniqueness property defined by Milchtaich (2005) as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions. He settled the case with two-terminal networks. As a corollary of his result, it is possible to prove that some other networks have the uniqueness property as well by adding common fictitious origin and destination. In the present work, we find a necessary condition for networks with several origin–destination pairs to have the uniqueness property in terms of excluded minors or subgraphs. As a key result, we characterize completely bidirectional rings for which the uniqueness property holds: it holds precisely for nine networks and those obtained from them by elementary operations. For other bidirectional rings, we exhibit affine cost functions yielding to two distinct equilibrium flows. Related results are also proven. For instance, we characterize networks having the uniqueness property for any choice of origin–destination pairs.     

Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator

We report on the bifurcation analysis of an extended Hindmarsh–Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its critical value. Applying the normal form theory, we derive a formula to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic flows. To observe this latter bifurcation and to illustrate its theoretical analysis, numerical simulations are performed. Hence, we present an explanation of the discontinuous behavior of the amplitude of the repetitive response as a function of system’s parameters based on the presence of the subcritical unstable oscillations. Furthermore, the bifurcation structures of the system are studied, with special care on the effects of parameters associated with the slow current and the slower dynamical process. We find that the system presents diversity of bifurcations such as period-doubling, symmetry breaking, crises and reverse period-doubling, when the afore mentioned parameters are varied in tiny steps. The complexity of the bifurcation structures seems useful to understand how neurons encode information or how they respond to external stimuli. Furthermore, we find that the extended Hindmarsh–Rose model also presents the multistability of oscillatory and silent regimes for precise sets of its parameters. This phenomenon plays a practical role in short-term memory and appears to give an evolutionary advantage for neurons since they constitute part of multifunctional microcircuits such as central pattern generators.     

An Application of Stochastic Programming with Weibull Distribution–Cluster Based Optimum Allocation of Recruitment in Manpower Planning

Abstract

Recruitment of persons for various assignments with required talents in an organization is an important feature, since it plays a vital role in the growth of the organization. To achieve the required expertise in recruitment, in this paper Linear Stochastic Programming (LSP) is applied along with cluster analysis technique. The aim of this paper is to obtain an optimal allocation of persons to different jobs, so that the time taken to complete all the jobs is minimum. The time taken for a person to complete a job is assumed to follow Weibull distribution. The parameters of Weibull distribution is obtained through Maximum Likelihood Estimator (MLE) approach, along with Cohen's iterative process.