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Does assortative mating lead to a polymorphic population? A toy model justification
Solution to a stochastic pursuit model using moment equations
1. | University of Białystok, Faculty of Mathematics and Informatics, K. Ciołkowskiego 1M, 15-245 Białystok, Poland |
2. | Kiev National Economics V. Hetman University Faculty of Information System and Technology, Kyiv 03068, Peremogy 54/1, Ukraine |
3. | Palacký University Olomouc, Faculty of Education, Žižkovo nám. 5, Olomouc, Czech Republic |
4. | Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry, Veveří 331/95,602 00 Brno, Czech Republic |
The paper investigates the navigation problem of following a moving target, using a mathematical model described by a system of differential equations with random parameters. The differential equations, which employ controls for following the target, are solved by a new approach using moment equations. Simulations are presented to test effectiveness of the approach.
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I. Dzhalladova, M. Růžičková, M. Štoudková and M. Růžičková,
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doi: 10.3934/dcdsb.2016087. |
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C. G. Guo, C. X. Guo, S. Ahmed and F. X. Liu,
Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays, Discrete Continuous Dynam. Systems -B, 21 (2016), 2473-2489.
doi: 10.3934/dcdsb.2016056. |
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J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, New York, 1987.
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M. Růžičková and I. Dzhalladova, The optimization of solutions of the dynamic systems with random structure Abstr. Appl. Anal. 2011 (2011), Art. ID 486714, 18 pp.
doi: 10.1155/2011/486714. |
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M. Šagát,
Stochastic Differential Equations and their Applications Mgr. thesis University of Žilina, Žilina -2814420132009,2013. |
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K. G. Valeev and I. Dzhalladova, Optimization of Random Processes, KNEU, Kiev, 2006.
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show all references
References:
[1] |
A. G. Aleksandrov, Optimal and Adaptive Systems, Nauka, Moscow, 1989.
![]() |
[2] |
J. Diblík, I. Dzhalladova, M. Michalková and M. Růžičková,
Modeling of applied problems by stochastic systems and their analysis using the moment equations, Adv. Difference Equ., 2013 (2013), 12 pp.
doi: 10.1186/1687-1847-2013-152. |
[3] |
J. Diblík, I. Dzhalladova, M. Michalková and M. Růžičková, Moment equations in modeling a stable foreign currency exchange market in conditions of uncertainty Abstr. Appl. Anal. 2013 (2013), Art. ID 172847, 11 pp.
doi: 10.1155/2013/172847. |
[4] |
I. A. Dzhalladova, Optimization of Stochastic System, KNEU, Kiev, 2005.
![]() |
[5] |
I. Dzhalladova, M. Růžičková, M. Štoudková and M. Růžičková,
Stability of the zero solution of nonlinear differential equations under the influence of white noise, Adv. Difference Equ., 2015 (2015), 11 pp.
doi: 10.1186/s13662-015-0482-y. |
[6] |
A. I. Egorov, Optimal Control with Linear Systems, KNEU, Kiev, 1988.
![]() |
[7] |
H. Gao and C. Sun,
Well-posedness of stochastic primitive equations with multiplicative noise in three dimensions, Discrete Continuous Dynam. Systems -B, 21 (2016), 3053-3073.
doi: 10.3934/dcdsb.2016087. |
[8] |
C. G. Guo, C. X. Guo, S. Ahmed and F. X. Liu,
Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with time-delays, Discrete Continuous Dynam. Systems -B, 21 (2016), 2473-2489.
doi: 10.3934/dcdsb.2016056. |
[9] |
J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, New York, 1987.
doi: 10.1007/978-3-662-02514-7.![]() ![]() ![]() |
[10] |
M. Růžičková and I. Dzhalladova, The optimization of solutions of the dynamic systems with random structure Abstr. Appl. Anal. 2011 (2011), Art. ID 486714, 18 pp.
doi: 10.1155/2011/486714. |
[11] |
M. Šagát,
Stochastic Differential Equations and their Applications Mgr. thesis University of Žilina, Žilina -2814420132009,2013. |
[12] |
K. G. Valeev and I. Dzhalladova, Optimization of Random Processes, KNEU, Kiev, 2006.
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