Nonlinear Dynamics, ISSN 0924-090X, 9/2017, Volume 89, Issue 4, pp. 2941 - 2955

.... When the economic threshold level is under the positive equilibrium, the existence, uniqueness and orbital asymptotical stability of order-1 periodic solution for the system can be obtained...

Engineering | Vibration, Dynamical Systems, Control | Leslie predatorâ€“prey system | Order-1 periodic solution | Successor function | Classical Mechanics | Automotive Engineering | Mechanical Engineering | State impulsive feedback control | Limit cycle | MULTIPLE DELAYS | GLOBAL STABILITY | Leslie predator-prey system | MODEL | ENGINEERING, MECHANICAL | MECHANICS | QUALITATIVE-ANALYSIS | FOOD-CHAIN SYSTEM | DYNAMICS | BIFURCATION | Numerical analysis | Differential equations | Predator-prey simulation | Computer simulation | Asymptotic properties | Differential geometry | Uniqueness | Orbital stability | Control systems | Feedback control | Equilibrium

Engineering | Vibration, Dynamical Systems, Control | Leslie predatorâ€“prey system | Order-1 periodic solution | Successor function | Classical Mechanics | Automotive Engineering | Mechanical Engineering | State impulsive feedback control | Limit cycle | MULTIPLE DELAYS | GLOBAL STABILITY | Leslie predator-prey system | MODEL | ENGINEERING, MECHANICAL | MECHANICS | QUALITATIVE-ANALYSIS | FOOD-CHAIN SYSTEM | DYNAMICS | BIFURCATION | Numerical analysis | Differential equations | Predator-prey simulation | Computer simulation | Asymptotic properties | Differential geometry | Uniqueness | Orbital stability | Control systems | Feedback control | Equilibrium

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 4/2014, Volume 76, Issue 2, pp. 1109 - 1117

.... We obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system (1.2...

Engineering | Vibration, Dynamical Systems, Control | Semicontinuous dynamic system | Order-1 periodic solution | Successor function | Mechanics | Heteroclinic bifurcation | Automotive Engineering | Mechanical Engineering | Order-1 heteroclinic cycle | MECHANICS | CHEMOSTAT MODEL | CONSEQUENCES | STATE-FEEDBACK CONTROL | ENGINEERING, MECHANICAL | Bifurcations | Nonlinear dynamics | Predators | Dynamics | Harvesting | Uniqueness | Mathematical models | Dynamical systems

Engineering | Vibration, Dynamical Systems, Control | Semicontinuous dynamic system | Order-1 periodic solution | Successor function | Mechanics | Heteroclinic bifurcation | Automotive Engineering | Mechanical Engineering | Order-1 heteroclinic cycle | MECHANICS | CHEMOSTAT MODEL | CONSEQUENCES | STATE-FEEDBACK CONTROL | ENGINEERING, MECHANICAL | Bifurcations | Nonlinear dynamics | Predators | Dynamics | Harvesting | Uniqueness | Mathematical models | Dynamical systems

Journal Article

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

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

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2017, Volume 53, Issue 1, pp. 471 - 486

In this paper, we aim to investigate the dynamics and existence of periodic solutions of a state-dependent impulsive model for continuous flow bioreactors...

Computational Mathematics and Numerical Analysis | Bioreactor | Order-1 periodic solution | Stability | 34C23 | Mathematics of Computing | Appl.Mathematics/Computational Methods of Engineering | 94D25 | Mathematics | Theory of Computation | Order-2 periodic solution | Impulsive model | SYSTEM | MATHEMATICS, APPLIED | PERTURBATIONS | mpulsive model | MEMBRANE REACTOR MODELS | PREDATOR | MATHEMATICS | PREY | KINETICS | DYNAMICS | FUNDAMENTAL ANALYSIS | Microorganisms | Models | Numerical analysis | Studies | Membrane reactors | Mathematical analysis | Applications of mathematics | Dynamic tests | Computer simulation | Bioreactors | Strategy | Mathematical models | Continuous flow

Computational Mathematics and Numerical Analysis | Bioreactor | Order-1 periodic solution | Stability | 34C23 | Mathematics of Computing | Appl.Mathematics/Computational Methods of Engineering | 94D25 | Mathematics | Theory of Computation | Order-2 periodic solution | Impulsive model | SYSTEM | MATHEMATICS, APPLIED | PERTURBATIONS | mpulsive model | MEMBRANE REACTOR MODELS | PREDATOR | MATHEMATICS | PREY | KINETICS | DYNAMICS | FUNDAMENTAL ANALYSIS | Microorganisms | Models | Numerical analysis | Studies | Membrane reactors | Mathematical analysis | Applications of mathematics | Dynamic tests | Computer simulation | Bioreactors | Strategy | Mathematical models | Continuous flow

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2014, Volume 78, Issue 1, pp. 743 - 753

The order-1 periodic solution of the system with impulsive state feedback control is investigated...

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | Stability | Mechanics | Automotive Engineering | Mechanical Engineering | Semi-continuous system | Existence | Impulsive state feedback control | MECHANICS | ENGINEERING, MECHANICAL | State feedback | Control systems | Stability analysis | Feedback control | Differential geometry | Differential equations | Nonlinear dynamics | Mathematical analysis | Referencing | Mathematical models | Dynamical systems

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | Stability | Mechanics | Automotive Engineering | Mechanical Engineering | Semi-continuous system | Existence | Impulsive state feedback control | MECHANICS | ENGINEERING, MECHANICAL | State feedback | Control systems | Stability analysis | Feedback control | Differential geometry | Differential equations | Nonlinear dynamics | Mathematical analysis | Referencing | Mathematical models | Dynamical systems

Journal Article

Advances in difference equations, ISSN 1687-1847, 2018, Volume 2018, Issue 1, pp. 1 - 13

.... Firstly, according to the differential equation geometry theory and the method of successor function, the existence, uniqueness and attractiveness of the order-1 periodic solution are analyzed...

34C25 | 34A37 | Order-1 periodic solution | 34D20 | Mathematics | Attractiveness | Ordinary Differential Equations | Functional Analysis | 92B05 | Analysis | Difference and Functional Equations | Mathematics, general | Successor functions | Partial Differential Equations | Semi-continuous dynamic systems | MATHEMATICS | MATHEMATICS, APPLIED | PEST-MANAGEMENT MODEL | FEEDBACK CONTROL | FEEDING SATURATION | PERIODIC-SOLUTION | Predator-prey simulation | Computer simulation | Differential geometry | Differential equations | Stability analysis | Mathematical models | Response functions

34C25 | 34A37 | Order-1 periodic solution | 34D20 | Mathematics | Attractiveness | Ordinary Differential Equations | Functional Analysis | 92B05 | Analysis | Difference and Functional Equations | Mathematics, general | Successor functions | Partial Differential Equations | Semi-continuous dynamic systems | MATHEMATICS | MATHEMATICS, APPLIED | PEST-MANAGEMENT MODEL | FEEDBACK CONTROL | FEEDING SATURATION | PERIODIC-SOLUTION | Predator-prey simulation | Computer simulation | Differential geometry | Differential equations | Stability analysis | Mathematical models | Response functions

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 8/2017, Volume 89, Issue 3, pp. 2001 - 2012

... . Moreover, the numerical simulations are provided to show the main results. The used methods are intuitive to prove the existence of order-1 periodic solution...

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | Homoclinic bifurcation | Successor function | Allee effect | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Order-1 homoclinic cycle | MANAGEMENT | CHEMOSTAT MODEL | ENGINEERING, MECHANICAL | MECHANICS | QUALITATIVE-ANALYSIS | DYNAMICS | BIOECONOMIC MODEL | STATE-FEEDBACK CONTROL | PERIODIC-SOLUTION | Analysis | Numerical analysis | Bifurcations | Control stability | Parameters | Predator-prey simulation | Computer simulation

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | Homoclinic bifurcation | Successor function | Allee effect | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Order-1 homoclinic cycle | MANAGEMENT | CHEMOSTAT MODEL | ENGINEERING, MECHANICAL | MECHANICS | QUALITATIVE-ANALYSIS | DYNAMICS | BIOECONOMIC MODEL | STATE-FEEDBACK CONTROL | PERIODIC-SOLUTION | Analysis | Numerical analysis | Bifurcations | Control stability | Parameters | Predator-prey simulation | Computer simulation

Journal Article

Advances in difference equations, ISSN 1687-1847, 2017, Volume 2017, Issue 1, pp. 1 - 17

... of natural enemies are linearly dependent on the given threshold in the second impulse. Firstly, the existence of order-1 periodic solution of the system is investigated...

34C25 | 34D20 | successor functions | Mathematics | order-1 periodic solution | Ordinary Differential Equations | Functional Analysis | 92B05 | optimization | Analysis | Difference and Functional Equations | Mathematics, general | semi-continuous dynamic systems | Partial Differential Equations | stability | SYSTEM | INFECTION DYNAMIC-MODEL | MATHEMATICS, APPLIED | PEST-MANAGEMENT MODEL | FEEDBACK CONTROL | CHEMOTAXIS | CHEMOSTAT MODEL | EPIDEMIC MODEL | DIFFERENTIAL-EQUATIONS | FUNCTIONAL-RESPONSE | MATHEMATICS | PERIODIC-SOLUTION | Theorems (Mathematics) | Usage | Mathematical analysis | Mathematical optimization | Mathematical models | Predator-prey simulation | Feedback control | Computer simulation | Spraying | Differential equations

34C25 | 34D20 | successor functions | Mathematics | order-1 periodic solution | Ordinary Differential Equations | Functional Analysis | 92B05 | optimization | Analysis | Difference and Functional Equations | Mathematics, general | semi-continuous dynamic systems | Partial Differential Equations | stability | SYSTEM | INFECTION DYNAMIC-MODEL | MATHEMATICS, APPLIED | PEST-MANAGEMENT MODEL | FEEDBACK CONTROL | CHEMOTAXIS | CHEMOSTAT MODEL | EPIDEMIC MODEL | DIFFERENTIAL-EQUATIONS | FUNCTIONAL-RESPONSE | MATHEMATICS | PERIODIC-SOLUTION | Theorems (Mathematics) | Usage | Mathematical analysis | Mathematical optimization | Mathematical models | Predator-prey simulation | Feedback control | Computer simulation | Spraying | Differential equations

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2016, Volume 87, Issue 3, pp. 1495 - 1509

... and orbital asymptotically stability of the order-1 periodic solution for the system with impulse effects...

Engineering | Vibration, Dynamical Systems, Control | Pest prevention and control | Order-1 periodic solution | Successor function | Classical Mechanics | Automotive Engineering | Orbital asymptotically stable | Mechanical Engineering | Impulsive state feedback control | PEST-MANAGEMENT MODEL | STABILITY | PERSISTENCE | TIME-DELAY | PESTICIDE | ENGINEERING, MECHANICAL | MECHANICS | PERMANENCE | DYNAMICS | OUTBREAK | PERIODIC-SOLUTION | Information science | Numerical analysis | Analysis | Differential equations | State feedback | Computer simulation | Asymptotic properties | Differential geometry | Spraying | Interference | Control systems | Feedback control | Predator-prey simulation | Mathematical analysis | Orbital stability | Qualitative analysis | Control stability | Nonlinear dynamics | Impulses | Mathematical models | Dynamical systems

Engineering | Vibration, Dynamical Systems, Control | Pest prevention and control | Order-1 periodic solution | Successor function | Classical Mechanics | Automotive Engineering | Orbital asymptotically stable | Mechanical Engineering | Impulsive state feedback control | PEST-MANAGEMENT MODEL | STABILITY | PERSISTENCE | TIME-DELAY | PESTICIDE | ENGINEERING, MECHANICAL | MECHANICS | PERMANENCE | DYNAMICS | OUTBREAK | PERIODIC-SOLUTION | Information science | Numerical analysis | Analysis | Differential equations | State feedback | Computer simulation | Asymptotic properties | Differential geometry | Spraying | Interference | Control systems | Feedback control | Predator-prey simulation | Mathematical analysis | Orbital stability | Qualitative analysis | Control stability | Nonlinear dynamics | Impulses | Mathematical models | Dynamical systems

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

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

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

The numbers of pests and of natural enemies released to control them as part of integrated pest management strategies are density dependent. Therefore, the...

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | PoincarĂ© map | Global stability | Classical Mechanics | Pest control | Automotive Engineering | Mechanical Engineering | Nonlinear control | COMPLEX DYNAMICS | PREDATOR-PREY MODEL | ENGINEERING, MECHANICAL | IMPULSIVE PERTURBATIONS | MECHANICS | LOTKA | VOLTERRA SYSTEMS | Poincare map | DELAY | EXTINCTION | Strategic planning (Business) | Information science | Yuan (China) | Analysis | Poincare maps | Nonlinear feedback | Tactics | Control systems | Feedback control | Pests | Insulin

Engineering | Vibration, Dynamical Systems, Control | Order-1 periodic solution | PoincarĂ© map | Global stability | Classical Mechanics | Pest control | Automotive Engineering | Mechanical Engineering | Nonlinear control | COMPLEX DYNAMICS | PREDATOR-PREY MODEL | ENGINEERING, MECHANICAL | IMPULSIVE PERTURBATIONS | MECHANICS | LOTKA | VOLTERRA SYSTEMS | Poincare map | DELAY | EXTINCTION | Strategic planning (Business) | Information science | Yuan (China) | Analysis | Poincare maps | Nonlinear feedback | Tactics | Control systems | Feedback control | Pests | Insulin

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 | Phytoplanktonâ€“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

Optimal harvesting | Order-1 periodic solution | Phytoplanktonâ€“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

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

order-1 cycle | semi-continuous | homoclinic cycle | Rotated vector fields | homoclinic bifurcation | EXISTENCE | STABILITY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL | PERIODIC-SOLUTION

Journal Article

16.
Full Text
Dynamic analysis of the ethanol fermentation with the impulsive state feedback control

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

....â€¢Existence and stability of the order-1 or order-2 periodic solution are investigated.â€¢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

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

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

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 02/2016, Volume 31, Issue 1-3, pp. 83 - 107

....â€¢Certain sufficient conditions for the existence and orbital stability of positive order-1 solution of the system are obtained...

Transgenic mosquitoes | Order-1 periodic solution | Pareto frontier | orbital stability | State-dependent impulsive perturbation | Pareto efficiency | Orbital stability | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | CONTROL STRATEGY | MODEL | PHYSICS, MATHEMATICAL | REFRACTORINESS | VECTOR | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ANOPHELES-STEPHENSI | DYNAMICS | Mosquitoes | Genetic engineering | Analysis | Anopheles | Numerical analysis | Genetically modified organisms

Transgenic mosquitoes | Order-1 periodic solution | Pareto frontier | orbital stability | State-dependent impulsive perturbation | Pareto efficiency | Orbital stability | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | CONTROL STRATEGY | MODEL | PHYSICS, MATHEMATICAL | REFRACTORINESS | VECTOR | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ANOPHELES-STEPHENSI | DYNAMICS | Mosquitoes | Genetic engineering | Analysis | Anopheles | Numerical analysis | Genetically modified organisms

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

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