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Indecision in Neural Decision Making Models

J. Milton, P. Naik, C. Chan, S. A. Campbell (2010)

Mathematical Modelling of Natural Phenomena

Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition....

Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations

I. Stojkovic, O. van Gaans (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.

Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations

Jianhui Huang, Jingtao Shi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic...

Multivalued backward stochastic differential equations with time delayed generators

Bakarime Diomande, Lucian Maticiuc (2014)

Open Mathematics

Our aim is to study the following new type of multivalued backward stochastic differential equation: - d Y t + ∂ φ Y t d t ∋ F t , Y t , Z t , Y t , Z t d t + Z t d W t , 0 ⩽ t ⩽ T , Y T = ξ , where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

Noise Shaping in Neural Populations with Global Delayed Feedback

O. Ávila Åkerberg, M. J. Chacron (2010)

Mathematical Modelling of Natural Phenomena

The interplay between intrinsic and network dynamics has been the focus of many investigations. Here we use a combination of theoretical and numerical approaches to study the effects of delayed global feedback on the information transmission properties of neural networks. Specifically, we compare networks of neurons that display intrinsic interspike interval correlations (nonrenewal) to networks that do not (renewal). We find that excitatory and...

Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations***

Shige Peng, Mingyu Xu (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations***

Shige Peng, Mingyu Xu (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Persistence and extinction of a stochastic delay predator-prey model under regime switching

Zhen Hai Liu, Qun Liu (2014)

Applications of Mathematics

The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.

Stability analysis for neutral stochastic systems with mixed delays

Huabin Chen, Peng Hu (2013)

Kybernetika

This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments. A new...

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