scholarly journals Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6452-6483
Author(s):  
Keguo Ren ◽  
◽  
Xining Li ◽  
Qimin Zhang ◽  
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Hamiltonian Function ◽  
Threshold Dynamics ◽  
Threshold Behavior ◽  
Necessary And Sufficient ◽  
Theoretical Results ◽  
Near Optimality

<abstract><p>Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns the near-optimal control of an avian influenza model with saturation on heterogeneous complex networks. Firstly, the basic reproduction number $ \mathcal{R}_{0} $ is defined for the model, which can be used to govern the threshold dynamics of influenza disease. Secondly, the near-optimal control problem was formulated by slaughtering poultry and treating infected humans while keeping the loss and cost to a minimum. Thanks to the maximum condition of the Hamiltonian function and the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality by several delicate estimates for the state and adjoint processes. Finally, a number of examples presented to illustrate our theoretical results.</p></abstract>

Near-optimal control problems for forward-backward regime-switching systems

2020 ◽  
Vol 26 ◽  
pp. 94
Author(s):  
Min Li ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Regime Switching ◽  
Hamiltonian Function ◽  
Minimum Condition ◽  
Optimal Controls ◽  
Diffusion Term ◽  
Finite State ◽  
Forward Diffusion ◽  
Theoretical Results ◽  
Near Optimality

This paper investigates the near-optimality for a class of forward-backward stochastic differential equations (FBSDEs) with continuous-time finite state Markov chains. The control domains are not necessarily convex and the control variables do not enter forward diffusion term. Some new estimates for state and adjoint processes arise naturally when we consider the near-optimal control problem in the framework of regime-switching. Inspired by Ekeland’s variational principle and a spike variational technique, the necessary conditions are derived, which imply the near-minimum condition of the Hamiltonian function in an integral sense. Meanwhile, some certain convexity conditions and the near-minimum condition are sufficient for the near-optimal controls with order ε1/2. A recursive utility investment consumption problem is discussed to illustrate the effectiveness of our theoretical results.

scholarly journals Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yue Zhang ◽  
Yuxuan Li
Keyword(s):  
Complex Networks ◽  
Numerical Experiments ◽  
Evolutionary Dynamics ◽  
Sufficient Conditions ◽  
Deterministic System ◽  
Stochastic Solution ◽  
Epidemic Dynamic ◽  
Theoretical Results ◽  
Disease Persistence ◽  
Human Awareness

In this paper, a stochastic SEIR (Susceptible-Exposed-Infected-Removed) epidemic dynamic model with migration and human awareness in complex networks is constructed. The awareness is described by an exponential function. The existence of global positive solutions for the stochastic system in complex networks is obtained. The sufficient conditions are presented for the extinction and persistence of the disease. Under the conditions of disease persistence, the distance between the stochastic solution and the local disease equilibrium of the corresponding deterministic system is estimated in the time sense. Some numerical experiments are also presented to illustrate the theoretical results. Although the awareness introduced in the model cannot affect the extinction of the disease, the scale of the disease will eventually decrease as human awareness increases.

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

Multiconsensus of first-order multiagent systems with directed topologies

2020 ◽  
Vol 34 (23) ◽  
pp. 2050240
Author(s):  
Xiao-Wen Zhao ◽  
Guangsong Han ◽  
Qiang Lai ◽  
Dandan Yue
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Problem ◽  
Multiple Agents ◽  
First Order ◽  
The Matrix ◽  
Directed Topologies ◽  
Necessary And Sufficient ◽  
Theoretical Results

The multiconsensus problem of first-order multiagent systems with directed topologies is studied. A novel consensus problem is introduced in multiagent systems — multiconsensus. The states of multiple agents in each subnetwork asymptotically converge to an individual consistent value in the presence of information exchanges among subnetworks. Linear multiconsensus protocols are proposed to solve the multiconsensus problem, and the matrix corresponding to the protocol is designed. Necessary and sufficient conditions are derived based on matrix theory, under which the stationary multiconsensus and dynamic multiconsensus can be reached. Simulations are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Linear-quadratic optimization and some general hypotheses on optimal control

1999 ◽  
Vol 5 (4) ◽  
pp. 275-289 ◽  
Author(s):  
L. I. Rozonoer
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Quadratic Optimization ◽  
Necessary And Sufficient Conditions ◽  
Maximum Condition ◽  
Linear Quadratic ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

Multivariate Simultaneous Generalized ARCH

1995 ◽  
Vol 11 (1) ◽  
pp. 122-150 ◽  
Author(s):  
Robert F. Engle ◽  
Kenneth F. Kroner
Keyword(s):  
Sufficient Conditions ◽  
Likelihood Estimation ◽  
Positive Definiteness ◽  
Covariance Matrices ◽  
Simultaneous Equations ◽  
Equivalence Relations ◽  
Conditional Covariance ◽  
Arch Models ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper presents theoretical results on the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed, and equivalence relations are discussed for the various ARCH parameterizations. Constraints sufficient to guarantee the positive definiteness of the conditional covariance matrices are developed, and necessary and sufficient conditions for covariance stationarity are presented. Identification and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

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