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order-1 periodic solution (26) 26
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Advances in difference equations, ISSN 1687-1847, 2018, Volume 2018, Issue 1, pp. 1 - 14
... are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed... 
34C25 | 34A37 | 34D20 | Mathematics | order-1 periodic solution | Ordinary Differential Equations | prey-predator model | Functional Analysis | 92B05 | optimization | Analysis | Difference and Functional Equations | state-dependent impulse | Mathematics, general | Partial Differential Equations | stability | SYSTEM | MATHEMATICS, APPLIED | HOMOCLINIC BIFURCATION | MATHEMATICS | GLOBAL DYNAMICS | DYNAMICS ANALYSIS | NONLINEAR PULSE | DELAY
Journal Article
Advances in difference equations, ISSN 1687-1847, 2018, Volume 2018, Issue 1, pp. 1 - 13
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 8/2017, Volume 89, Issue 3, pp. 2001 - 2012
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2018, Volume 491, pp. 516 - 527
.... By the successor function, the sufficient conditions for the existence and uniqueness of order-1 periodic solution are presented first... 
Order-1 periodic solution | Successor function | State dependent impulsive control | Media coverage | Spread of computer virus | PHYSICS, MULTIDISCIPLINARY | STABILITY | NETWORKS | INFECTION | PREVALENCE | SPREAD | Models | Numerical analysis | Computer viruses | Analysis
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 8/2016, Volume 85, Issue 3, pp. 1561 - 1569
.... The existence of order-1 periodic solution and its stability were proved with a novel method. The results demonstrated that the application of software patches is an effective approach to constrain the deluge of computer worm... 
Engineering | Vibration, Dynamical Systems, Control | State feedback | Computer worm | Order-1 periodic solution | Impulse model | Mechanics | Automotive Engineering | Mechanical Engineering | Semi-continuous system | MECHANICS | GLOBAL STABILITY | VIRUSES | ENGINEERING, MECHANICAL | Forests and forestry | Models | Numerical analysis | Computer viruses | Analysis | Computer worms | Computer simulation | Mathematical models | Patching | Software | Software upgrading
Journal Article
Nonlinear dynamics, ISSN 1573-269X, 2018, Volume 94, Issue 3, pp. 2243 - 2263
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 05/2017, Volume 88, Issue 3, pp. 2003 - 2011
... of the order-1 periodic solution by means of successor function. The stability of the order-1 periodic solution is discussed by a novel stability criterion on the basis of the stability theory of limit cycle... 
Optimal harvesting | Order-1 periodic solution | Phytoplankton–fish model | Impulsive feedback control | Phytoplankton-fish model | MECHANICS | RESERVE AREA | ZOOPLANKTON | ENGINEERING, MECHANICAL | RESOURCE | Information science | Models | Numerical analysis | Analysis | Plankton | Computer simulation | Stability criteria | Optimal control | Control systems | Maximum principle | Phytoplankton | Fish | Feedback control
Journal Article
Journal of Applied Mathematics and Computing, ISSN 1598-5865, 6/2015, Volume 48, Issue 1, pp. 205 - 219
... of the corresponding continuous system. We prove that ethanol fermentation with impulsive state feedback control tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the fermentation... 
34C05 | Computational Mathematics and Numerical Analysis | Ethanol inhibition | Order-1 periodic solution | 92D25 | Mathematics of Computing | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Theory of Computation | Feedback control | Order-2 periodic solution | Alcohol | Analysis | Alcohol, Denatured | Studies | Mathematical models | Ethanol | Fermentation | Differential equations | State feedback | Computer simulation | Ethyl alcohol | Nonlinearity | Models
Journal Article
International Journal of Biomathematics, ISSN 1793-5245, 11/2012, Volume 5, Issue 6
.... On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed... 
order-1 cycle | semi-continuous | homoclinic cycle | Rotated vector fields | homoclinic bifurcation | EXISTENCE | STABILITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL | PERIODIC-SOLUTION
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 02/2016, Volume 83, pp. 274 - 281
....•Existence and stability of the order-1 or order-2 periodic solution are investigated.•The complete expression of the order-1 periodic solution is obtained... 
Order-1 periodic solution | Feedback control | Order-2 periodic solution | Stability of the periodic solution | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Alcohol | Alcohol, Denatured | Fermentation | Analysis
Journal Article
International Journal of Biomathematics, ISSN 1793-5245, 11/2018, Volume 11, Issue 8
.... The sufficient conditions of existence of order-1 periodic solution are obtained in view of the geometrical theory of the semi-continuous dynamical system and the qualitative properties... 
drug-sensitivity strain | drug-resistant strain | order-1 periodic solution | Impulsive state feedback control | FUNGAL-INFECTION | SYSTEM | IMMUNE COMPROMISED INDIVIDUALS | MUTATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL | STATE-FEEDBACK CONTROL
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 06/2016, Volume 87, pp. 255 - 261
.... The sufficient conditions for the existence of the order-1 and order-2 periodic solutions are obtained by using the geometrical theory of semi-continuous dynamic system... 
Semi-continuous dynamic system | Order-1 periodic solution | Plankton | Order-2 periodic solution | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | BIFURCATION | Analysis | Models | Numerical analysis
Journal Article