Browsing by Author "Abbas, Syed"

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Citation - WoS: 6
Citation - Scopus: 6
On optimal solutions of general continuous-singular stochastic control problem of McKean-Vlasov type
(WILEY, 2020) Lina Guenane; Mokhtar Hafayed; Shahlar Meherrem; Syed Abbas; Guenane, Lina; Hafayed, Mokhtar; Meherrem, Shahlar; Abbas, Syed
In this paper we establish general necessary optimality conditions for stochastic continuous-singular control of McKean-Vlasov type equations. The coefficients of the state equation depend on the state of the solution process as well as of its probability law and the control variable. The coefficients of the system are nonlinear and depend explicitly on the absolutely continuous component of the control. The control domain under consideration is not assumed to be convex. The proof of our main result is based on the first- and second-order derivatives with respect to measure in Wasserstein space of probability measures and by using variational method.
Citation - WoS: 2
Citation - Scopus: 2
On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes
(INDERSCIENCE ENTERPRISES LTD, 2019) Shahlar Meherrem; Mokhtar Hafayed; Syed Abbas; Hafayed, Mokhtar; Meherrem, Shahlar; Abbas, Syed
In this paper we investigate the Peng's type optimal control problems for stochastic differential equations of mean-field type with jump processes. The coefficients of the system contain not only the state process but also its marginal distribution through their expected values. We assume that the control set is a general open set that is not necessary convex. The control variable is allowed to enter into both diffusion and jump terms. We extend the maximum principle of Buckdahn et al. (2011) to jump case.
Citation - WoS: 13
Citation - Scopus: 13
Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term
(Elsevier B.V., 2018) Swati Tyagi; Subit K. Jain; Syed Abbas; Shahlar Meherrem; Rajendra K. Ray; Ray, Rajendra K.; Jain, Subit K.; Tyagi, Swati; Meherrem, Shahlar; Abbas, Syed
In this paper we consider a general 2-neuron network model with reaction–diffusion term and time delay. We study the effect of time delay in kinetic terms of reaction–diffusive system. We mainly investigate the effects of time delay and diffusion term on the stability of the neural network model. Later we present an algorithm to determine the existence of Hopf bifurcation for the delayed system with reaction–diffusion term along with Neumann boundary conditions. We determine the conditions on the delay parameter for the Hopf bifurcation to exist corresponding to the characteristic equation obtained by linearization of system. At the end we give some numerical examples along with simulation results to show effectiveness of our analytic findings. © 2018 Elsevier B.V. All rights reserved.