Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123627

The Toda equation, which has applications in many fields, is one of the most important integrable systems. A generalization of the Toda equation is the...

Hungry Lotka-Volterra system | Kostant-Toda equation | Integrable systems | Hungry Toda equation | Lower Hessenberg matrices

Hungry Lotka-Volterra system | Kostant-Toda equation | Integrable systems | Hungry Toda equation | Lower Hessenberg matrices

Journal Article

Journal of Theoretical Biology, ISSN 0022-5193, 12/2018, Volume 458, pp. 47 - 57

We propose Lotkaâ€“Volterra type predator-prey equations which include small constant terms. Depending on its sign, the constant may model various things. To see...

Lotkaâ€“Volterra equations | Predator-prey equations | Patchiness | Turing patterns | SYSTEM | STOCKING | PATCHY INVASION | MODEL | Lotka-Volterra equations | PATTERN-FORMATION | SPATIOTEMPORAL COMPLEXITY | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | DIFFUSION | STABILITY REGIONS

Lotkaâ€“Volterra equations | Predator-prey equations | Patchiness | Turing patterns | SYSTEM | STOCKING | PATCHY INVASION | MODEL | Lotka-Volterra equations | PATTERN-FORMATION | SPATIOTEMPORAL COMPLEXITY | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | DIFFUSION | STABILITY REGIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 9, pp. 4724 - 4770

In this paper, we study the traveling wave solutions and minimal wave speed for a class of non-cooperative reactionâ€“diffusion systems consisting of three...

Persistence theory | LaSalle's invariance principle | Minimal wave speed | Applications | Three equations | EXISTENCE | PREDATOR-PREY SYSTEMS | EPIDEMIC MODEL | MONOTONICITY | TRAVELING-WAVES | MATHEMATICS | DIFFERENTIAL INFECTIVITY | TRANSMISSION | NONLINEAR INCIDENCE | DYNAMIC-BEHAVIOR | LOTKA-VOLTERRA EQUATIONS | Mortality | Analysis

Persistence theory | LaSalle's invariance principle | Minimal wave speed | Applications | Three equations | EXISTENCE | PREDATOR-PREY SYSTEMS | EPIDEMIC MODEL | MONOTONICITY | TRAVELING-WAVES | MATHEMATICS | DIFFERENTIAL INFECTIVITY | TRANSMISSION | NONLINEAR INCIDENCE | DYNAMIC-BEHAVIOR | LOTKA-VOLTERRA EQUATIONS | Mortality | Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 299, pp. 429 - 445

Reactionâ€“diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such...

Stochastic model | Reactionâ€“diffusion system | Lotkaâ€“Volterra equation | Hybrid model | Fisherâ€“Kolmogorov equation | Reaction-diffusion system | Fisher-Kolmogorov equation | Lotka-Volterra equation | ALGORITHM REFINEMENT | COUPLED CHEMICAL-REACTIONS | NOISE | TIME | SIMULATION | PHYSICS, MATHEMATICAL | INVASION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | SYSTEMS | PROPAGATION | Analysis | Models | Biomedical engineering | Computer simulation | Partial differential equations | Preserves | Lattice sites | Bacteria | Ecology | Mathematical models | Stochasticity | FOKKER-PLANCK EQUATION | BACTERIA | DIFFUSION EQUATIONS | ERRORS | STOCHASTIC PROCESSES | PARTICLES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | VOLTERRA INTEGRAL EQUATIONS | COMPUTERIZED SIMULATION | MOLECULES | CHAPMAN-KOLMOGOROV EQUATION | DETERMINISTIC ESTIMATION | MEAN-FIELD THEORY | ATOMS

Stochastic model | Reactionâ€“diffusion system | Lotkaâ€“Volterra equation | Hybrid model | Fisherâ€“Kolmogorov equation | Reaction-diffusion system | Fisher-Kolmogorov equation | Lotka-Volterra equation | ALGORITHM REFINEMENT | COUPLED CHEMICAL-REACTIONS | NOISE | TIME | SIMULATION | PHYSICS, MATHEMATICAL | INVASION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | SYSTEMS | PROPAGATION | Analysis | Models | Biomedical engineering | Computer simulation | Partial differential equations | Preserves | Lattice sites | Bacteria | Ecology | Mathematical models | Stochasticity | FOKKER-PLANCK EQUATION | BACTERIA | DIFFUSION EQUATIONS | ERRORS | STOCHASTIC PROCESSES | PARTICLES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | VOLTERRA INTEGRAL EQUATIONS | COMPUTERIZED SIMULATION | MOLECULES | CHAPMAN-KOLMOGOROV EQUATION | DETERMINISTIC ESTIMATION | MEAN-FIELD THEORY | ATOMS

Journal Article

Journal of Mechanical Design, Transactions of the ASME, ISSN 1050-0472, 06/2018, Volume 140, Issue 6

During the development planning of a new product, designers and entrepreneurs rely on the prediction of product performance to make business investment and...

product performance | technology evolution | Lotka-Volterra equations | product development planning | technology prediction | technological forecasting | COMPETITION | ENGINEERING, MECHANICAL

product performance | technology evolution | Lotka-Volterra equations | product development planning | technology prediction | technological forecasting | COMPETITION | ENGINEERING, MECHANICAL

Journal Article

Journal of Theoretical Biology, ISSN 0022-5193, 2011, Volume 277, Issue 1, pp. 1 - 6

The article presents the solutions of Lotkaâ€“Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem...

Fractional time derivative | Homotopy perturbation method | Initial value problem | Lotkaâ€“Volterra model | Lotka-Volterra model | PREDATOR-PREY DYNAMICS | ORDER | NONLINEAR PROBLEMS | PARTIAL-DIFFERENTIAL-EQUATIONS | PARAMETRIC ANALYSIS | THEORETICAL STABILITY | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | APPROXIMATE ANALYTICAL SOLUTION | LIMIT-CYCLES | Predatory Behavior - physiology | Animals | Numerical Analysis, Computer-Assisted | Models, Biological

Fractional time derivative | Homotopy perturbation method | Initial value problem | Lotkaâ€“Volterra model | Lotka-Volterra model | PREDATOR-PREY DYNAMICS | ORDER | NONLINEAR PROBLEMS | PARTIAL-DIFFERENTIAL-EQUATIONS | PARAMETRIC ANALYSIS | THEORETICAL STABILITY | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | APPROXIMATE ANALYTICAL SOLUTION | LIMIT-CYCLES | Predatory Behavior - physiology | Animals | Numerical Analysis, Computer-Assisted | Models, Biological

Journal Article

7.
Full Text
Generalized system of trial equation methods and their applications to biological systems

Applied Mathematics and Computation, ISSN 0096-3003, 12/2018, Volume 338, pp. 722 - 732

It is shown that many systems of nonlinear differential equations of interest in various fields are naturally embedded in a new family of differential...

Ebola virus | Trial equation method | Lotkaâ€“Volterra | SIR | Nonlinear system differential equations | MATHEMATICS, APPLIED | Lotka-Volterra

Ebola virus | Trial equation method | Lotkaâ€“Volterra | SIR | Nonlinear system differential equations | MATHEMATICS, APPLIED | Lotka-Volterra

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 07/2017, Volume 263, Issue 1, pp. 687 - 708

We consider the problem where denotes the unit ball in , ( ), , and . We study the existence, multiplicity and uniqueness of radially symmetric bounded...

k-Hessian operator | Radial solutions | Phase analysis | Lotkaâ€“Volterra system | Critical exponents | EXISTENCE | BALL | POSITIVE SOLUTIONS | Lotka-Volterra system | MATHEMATICS | EIGENVALUES | QUADRATIC SYSTEMS | THEOREMS | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS | OPERATORS | DOMAINS

k-Hessian operator | Radial solutions | Phase analysis | Lotkaâ€“Volterra system | Critical exponents | EXISTENCE | BALL | POSITIVE SOLUTIONS | Lotka-Volterra system | MATHEMATICS | EIGENVALUES | QUADRATIC SYSTEMS | THEOREMS | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS | OPERATORS | DOMAINS

Journal Article

International Journal of Low Radiation, ISSN 1477-6545, 2016, Volume 10, Issue 3, pp. 222 - 233

The paper presents the concept of balance equation as a result of jostling process between detrimental and beneficial factors due to ionising radiation impact...

Evolution | Lotka-Volterra | Balance equation | Low dose | Radiation | Predator-prey simulation | Thresholds | Mathematical analysis | Paper | Mathematical models | Lotka-Volterra equations

Evolution | Lotka-Volterra | Balance equation | Low dose | Radiation | Predator-prey simulation | Thresholds | Mathematical analysis | Paper | Mathematical models | Lotka-Volterra equations

Journal Article

Journal of Theoretical Biology, ISSN 0022-5193, 09/2016, Volume 404, pp. 383 - 390

The replicator equation has been frequently used in the theoretical literature to explain a diverse array of biological phenomena. However, it makes several...

Replicator dynamics | Truncation selection | ESS | Cooperation | Evolutionary game theory | GAME DYNAMICS | FINITE POPULATIONS | STABILITY | CLASSIFICATION | EVOLUTIONARY STABLE STRATEGIES | GRAPHS | LOTKA-VOLTERRA EQUATION | NATURAL-SELECTION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Biological Evolution | Game Theory | Time Factors | Models, Biological | Systems Analysis | Computer Simulation | Selection, Genetic | Game theory | Analysis

Replicator dynamics | Truncation selection | ESS | Cooperation | Evolutionary game theory | GAME DYNAMICS | FINITE POPULATIONS | STABILITY | CLASSIFICATION | EVOLUTIONARY STABLE STRATEGIES | GRAPHS | LOTKA-VOLTERRA EQUATION | NATURAL-SELECTION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Biological Evolution | Game Theory | Time Factors | Models, Biological | Systems Analysis | Computer Simulation | Selection, Genetic | Game theory | Analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 323, Issue 2, pp. 938 - 957

In this paper, we consider the evolution of a system composed of two predatorâ€“prey deterministic systems described by Lotkaâ€“Volterra equations in random...

Telegraph noise | Predatorâ€“prey model | Lotkaâ€“Volterra equation | Predator-prey model | Lotka-Volterra equation | MATHEMATICS | predator-prey model | POPULATION | COEXISTENCE | MATHEMATICS, APPLIED | telegraph noise | BEHAVIOR | Analysis | Universities and colleges

Telegraph noise | Predatorâ€“prey model | Lotkaâ€“Volterra equation | Predator-prey model | Lotka-Volterra equation | MATHEMATICS | predator-prey model | POPULATION | COEXISTENCE | MATHEMATICS, APPLIED | telegraph noise | BEHAVIOR | Analysis | Universities and colleges

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 02/2014, Volume 83, Issue 2, pp. 1 - 1

In this paper, a new n-dimensional homogeneous Lotka-Volterra (HLV) equation, which possesses a Lie symmetry, is derived by the extension from a...

Algebra | Predator-prey simulation | Integral equations | Mathematical analysis | Lotka-Volterra equations | Dynamical systems | Three dimensional | Symmetry

Algebra | Predator-prey simulation | Integral equations | Mathematical analysis | Lotka-Volterra equations | Dynamical systems | Three dimensional | Symmetry

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2001, Volume 42, Issue 10, pp. 4984 - 4996

A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and...

CASIMIR INVARIANTS | GENERALIZED HAMILTONIAN-STRUCTURE | ENERGY-MOMENTUM METHOD | BRACKETS | DYNAMICAL-SYSTEMS | STABILITY | POLARIZATION DYNAMICS | LOTKA-VOLTERRA EQUATIONS | MAGNETOHYDRODYNAMICS | PHYSICS, MATHEMATICAL | RELATIVE EQUILIBRIA

CASIMIR INVARIANTS | GENERALIZED HAMILTONIAN-STRUCTURE | ENERGY-MOMENTUM METHOD | BRACKETS | DYNAMICAL-SYSTEMS | STABILITY | POLARIZATION DYNAMICS | LOTKA-VOLTERRA EQUATIONS | MAGNETOHYDRODYNAMICS | PHYSICS, MATHEMATICAL | RELATIVE EQUILIBRIA

Journal Article

REVISTA MATEMATICA IBEROAMERICANA, ISSN 0213-2230, 2019, Volume 35, Issue 5, pp. 1559 - 1582

The aim of this paper is to deal with the k-Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the...

EXISTENCE | POSITIVE SOLUTIONS | phase analysis | non-autonomous Lotka-Volterra system | MATHEMATICS | EIGENVALUES | singular solution | radial solutions | k-Hessian operator | DIRICHLET PROBLEM | critical exponents | ELLIPTIC-EQUATIONS | intersection number

EXISTENCE | POSITIVE SOLUTIONS | phase analysis | non-autonomous Lotka-Volterra system | MATHEMATICS | EIGENVALUES | singular solution | radial solutions | k-Hessian operator | DIRICHLET PROBLEM | critical exponents | ELLIPTIC-EQUATIONS | intersection number

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 04/2012, Volume 241, Issue 7, pp. 764 - 774

A new family of solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is investigated. This family is mathematically...

Poisson structures | Casimir invariants | Jacobi partial differential equations | Finite-dimensional Poisson systems | MATHEMATICS, APPLIED | DIMENSIONAL POISSON SYSTEMS | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | BI-HAMILTONIAN STRUCTURE | CLASSIFICATION | FORMULATION | PHYSICS, MATHEMATICAL | FAMILY | DYNAMICAL-SYSTEMS | LOTKA-VOLTERRA EQUATIONS | TODA | Differential equations | Construction | Infinity | Partial differential equations | Mathematical analysis | Focusing | Canonical forms | Nonlinearity | Invariants

Poisson structures | Casimir invariants | Jacobi partial differential equations | Finite-dimensional Poisson systems | MATHEMATICS, APPLIED | DIMENSIONAL POISSON SYSTEMS | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | BI-HAMILTONIAN STRUCTURE | CLASSIFICATION | FORMULATION | PHYSICS, MATHEMATICAL | FAMILY | DYNAMICAL-SYSTEMS | LOTKA-VOLTERRA EQUATIONS | TODA | Differential equations | Construction | Infinity | Partial differential equations | Mathematical analysis | Focusing | Canonical forms | Nonlinearity | Invariants

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2009, Volume 40, Issue 6, pp. 2217 - 2240

We deal with a system of Lotka-Volterra competition-diffusion equations on R, which is a competing two species model with diffusion. It is known that the...

Competition-diffusion | Entire solution | Traveling wave | Lotka-Volterra | traveling wave | EXISTENCE | FRONTS | MATHEMATICS, APPLIED | competition-diffusion | TRAVELING-WAVE SOLUTIONS | STABILITY | entire solution | Predator-prey simulation | Wave propagation | Dynamics | Extinction | Mathematical analysis | Mathematical models | Diffusion | Lotka-Volterra equations

Competition-diffusion | Entire solution | Traveling wave | Lotka-Volterra | traveling wave | EXISTENCE | FRONTS | MATHEMATICS, APPLIED | competition-diffusion | TRAVELING-WAVE SOLUTIONS | STABILITY | entire solution | Predator-prey simulation | Wave propagation | Dynamics | Extinction | Mathematical analysis | Mathematical models | Diffusion | Lotka-Volterra equations

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2011, Volume 33, Issue 3, pp. 1234 - 1245

The molecule solution of an equation related to the lattice Boussinesq equation is derived with the help of determinantal identities. It is shown that this...

Convergence acceleration algorithm | Lattice Boussinesq equation | Molecule solution | EXTRAPOLATION | MATHEMATICS, APPLIED | molecule solution | lattice Boussinesq equation | TODA MOLECULE | LOTKA-VOLTERRA SYSTEM | convergence acceleration algorithm | LAPLACE | Studies | Lattice theory | Algorithms | Numerical analysis

Convergence acceleration algorithm | Lattice Boussinesq equation | Molecule solution | EXTRAPOLATION | MATHEMATICS, APPLIED | molecule solution | lattice Boussinesq equation | TODA MOLECULE | LOTKA-VOLTERRA SYSTEM | convergence acceleration algorithm | LAPLACE | Studies | Lattice theory | Algorithms | Numerical analysis

Journal Article

International Biodeterioration & Biodegradation, ISSN 0964-8305, 11/2016, Volume 115, pp. 49 - 54

Aerobic granulation is a special form of biofilm growth and is the process of microbial immobilization. Selection pressure resulted from sedimentation and...

Competition | Lotkaâ€“Volterra equation | Aerobic granulation | Selective pressure | Modeling | ORGANIC LOADING RATE | ACTIVATED-SLUDGE | STABILITY | Lotka-Volterra equation | GRANULES | ENVIRONMENTAL SCIENCES | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | WASTE-WATER | SELECTION PRESSURE | GROWTH | DYNAMICS | OPTIMIZATION

Competition | Lotkaâ€“Volterra equation | Aerobic granulation | Selective pressure | Modeling | ORGANIC LOADING RATE | ACTIVATED-SLUDGE | STABILITY | Lotka-Volterra equation | GRANULES | ENVIRONMENTAL SCIENCES | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | WASTE-WATER | SELECTION PRESSURE | GROWTH | DYNAMICS | OPTIMIZATION

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2007, Volume 48, Issue 2, pp. 022903 - 022903-11

A new family of skew-symmetric solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is characterized and analyzed....

CASIMIR INVARIANTS | GENERALIZED HAMILTONIAN STRUCTURES | BRACKETS | QUADRATIC POISSON STRUCTURES | IDENTITIES | DYNAMICAL-SYSTEMS | CONSTRUCTION | LOTKA-VOLTERRA EQUATIONS | MAGNETOHYDRODYNAMICS | FORMULATION | PHYSICS, MATHEMATICAL

CASIMIR INVARIANTS | GENERALIZED HAMILTONIAN STRUCTURES | BRACKETS | QUADRATIC POISSON STRUCTURES | IDENTITIES | DYNAMICAL-SYSTEMS | CONSTRUCTION | LOTKA-VOLTERRA EQUATIONS | MAGNETOHYDRODYNAMICS | FORMULATION | PHYSICS, MATHEMATICAL

Journal Article

20.