Hamiltonian structure and first integrals for the Lotka-Volterra systems
From MaRDI portal
Publication:997697
DOI10.1016/S0375-9601(00)00454-0zbMath1115.34303MaRDI QIDQ997697
Publication date: 7 August 2007
Published in: Physics Letters. A (Search for Journal in Brave)
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Related Items (25)
$3D$-flows generated by the curl of a vector potential & Maurer-Cartan equations ⋮ On a Hamiltonian version of a three-dimensional Lotka-Volterra system ⋮ Geometrical aspects of the hamiltonization problem of dynamical systems ⋮ Explicit expression for a first integral for some classes of two-dimensional differential systems ⋮ Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems ⋮ Complex dynamics in the stretch-twist-fold flow ⋮ Bi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvature ⋮ Existence of almost-periodic solutions for Lotka-Volterra cooperative systems with time delay ⋮ Unnamed Item ⋮ On the dynamics of a class of Kolmogorov systems ⋮ Almost periodic solution for a delayed Lotka-Volterra system on time scales ⋮ Positive periodic solutions of delayed periodic Lotka-Volterra systems ⋮ On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems ⋮ Integrable deformations of Lotka-Volterra systems ⋮ New solutions of the Jacobi equations for three-dimensional Poisson structures ⋮ Characterization and global analysis of a family of Poisson structures ⋮ One solution of the 3D Jacobi identities allows determining an infinity of them ⋮ Almost periodic solutions for Lotka-Volterra systems with delays ⋮ Unnamed Item ⋮ On the dynamics of a class of rational Kolmogorov systems ⋮ Lotka-Volterra Systems with Periodic Orbits ⋮ On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D ⋮ Lotka–Volterra systems integrable in quadratures ⋮ On the Dynamics of a Class of Kolmogorov Systems ⋮ A Class of Quintic Kolmogorov Systems with Explicit Non-algebraic Limit Cycle
Cites Work
- Unnamed Item
- Unnamed Item
- Integrals of quadratic ordinary differential equations in \(\mathbb R^3\): the Lotka-Volterra system
- An indirect method of finding integrals for three-dimensional quadratic homogeneous systems
- Direct integration method and first integrals for three-dimensional Lotka-Volterra systems
- Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
- Poisson structure of dynamical systems with three degrees of freedom
- Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
- Hamiltonian structures for the n-dimensional Lotka–Volterra equations
This page was built for publication: Hamiltonian structure and first integrals for the Lotka-Volterra systems
