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Journal of Theoretical Biology, ISSN 0022-5193, 12/2018, Volume 458, pp. 47 - 57
We propose Lotka–Volterra type predator-prey equations which include small constant terms. Depending on its sign, the constant may model various things. To see... 
Lotka–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 reaction–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
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
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 2011, Volume 277, Issue 1, pp. 1 - 6
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
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 04/2012, Volume 241, Issue 7, pp. 764 - 774
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
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
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 02/2006, Volume 47, Issue 2, pp. 022901 - 022901-13
A four-dimensional family of skew-symmetric solutions of the Jacobi equations for Poisson structures is characterized. As a consequence, previously known types... 
CASIMIR INVARIANTS | GENERALIZED HAMILTONIAN STRUCTURES | VARIATIONAL-PRINCIPLES | MOTION | 1ST INTEGRALS | DYNAMICAL-SYSTEMS | CONSTRUCTION | LOTKA-VOLTERRA EQUATIONS | MAGNETOHYDRODYNAMICS | FORMULATION | PHYSICS, MATHEMATICAL
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2018, Volume 2018, Issue 48, pp. 1 - 19
Geometric integrators are numerical methods for differential equations that preserve geometric properties. In this article we investigate the questions of... 
Hamilton systems | Operator splitting | Lotka-Volterra equations | Numerical methods | MATHEMATICS | MATHEMATICS, APPLIED | numerical methods | operator splitting | hamilton systems | lotka–volterra equations
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2020, Volume 268, Issue 6, pp. 2551 - 2586
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 01/2011, Volume 36, Issue 6, pp. 1071 - 1098
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the... 
Adaptive evolution | Hamilton-Jacobi equation | 35F21 | 47G20 | Lotka-Volterra parabolic equation | 92D15 | Dirac concentrations | 49L25 | 35K55 | PDE | MATHEMATICS | MATHEMATICS, APPLIED | HAMILTON-JACOBI EQUATIONS | ADAPTIVE DYNAMICS | Partial differential equations | Evolution | Evolution & development
Journal Article
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 | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATIONS | LATTICE | integrable systems
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2001, Volume 256, Issue 1, pp. 242 - 256
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 07/2014, Volume 55, Issue 2, pp. 319 - 340
Over the last decade, the field of geometric integration has rapidly established itself as one of the core research areas in numerical ordinary differential... 
Lotka–Volterra equations | Poisson integrators | Positivity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Lotka-Volterra equations
Journal Article
International Journal of Bifurcation and Chaos, ISSN 0218-1274, 09/2016, Volume 26, Issue 10, p. 1650164
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 07/2019, Volume 124, pp. 105 - 124
Journal Article