A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle

The institutional investor selling a large block of shares in the market usually faces with liquidity risk declining the stock’s prices. In the paper, supposing that temporary impact is stochastic and nonlinear function of trading velocity, we establishes the discrete mathematical model and uses PSO to obtain the optimal liquidation strategies of risk aversion, which is a strict concave function. When analyzing the sensitivity of the parameters, we find that the curve becomes higher and steeper with the increase of the parameters or the decrease of , .As the parameter is tremendous, the curve is close to a horizon line.

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Equilibrium and business cycle. Mathematical model

Studia i Prace WNEiZ ◽

10.18276/sip.2018.51/3-16 ◽

2018 ◽

Vol 51 ◽

pp. 197-211

Author(s):

Robert Kruszewski

Keyword(s):

Mathematical Model ◽

Business Cycle

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Marine Oil Spill Control Based on Discrete Mathematical Model

Journal of Coastal Research ◽

10.2112/si103-079.1 ◽

2020 ◽

Vol 103 (sp1) ◽

pp. 387

Author(s):

Yang Liu

Keyword(s):

Mathematical Model ◽

Oil Spill ◽

Marine Oil ◽

Spill Control ◽

Discrete Mathematical Model

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Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501175 ◽

2020 ◽

Vol 30 (08) ◽

pp. 2050117

Author(s):

Marcelo Messias ◽

Rafael Paulino Silva

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Simple Form ◽

Chaotic Dynamics ◽

Third Order ◽

Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

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