RESEARCH INTERESTS

• Nonlinear Dynamical Systems

Keywords: Quasipolynomial formalism, quasipolynomial systems, Lotka-Volterra systems, quasimonomial transformations, nonlinearity, integrability, invariants, first integrals, stability, Liapunov functions, LaSalle  theorem, global behaviour, connectionism, algebraic methods.

• Population Dynamics (Lotka-Volterra Models and their Generalizations)                   

Keywords: Lotka-Volterra systems, generalized Lotka-Volterra systems, quasipolynomial systems, power-law models, kinetic equations, mass-action equations, population modelling, interspecific interactions, intraspecific interactions, trophic web, stability, complexity, connectionism, reaction-diffusion models, Fisher-KPP equation, ecological models.

• Biochemical Systems Theory

Keywords: S-systems, generalized mass-action (GMA) systems, power-law formalism, metabolic pahtways, kinetic equations, reaction equations, metabolic modelling, integrative modelling, simulation, sensitivity analysis, stability, nonlinear optimization.

• Hamiltonian and Poisson Systems

Keywords: Conservative systems, conservative Lotka-Volterra equations, finite-dimensional Hamiltonian and Poisson systems, generalized Hamiltonian systems, integrability, Casimir invariants, stability, Liapunov functions, energy-Casimir method, Jacobi identities for Poisson systems (Jacobi PDEs), Darboux Theorem, Darboux reduction, symplectic leaves, symplectic structure, Poisson brackets.

• Discrete-Time Systems (Nonlinear Maps)

Keywords: Ricker maps (exponential maps), Lotka-Volterra maps, quasipolynomial maps, nonoverlapping generations, discretization, algebraic methods, stability, chaos, permanence, dissipativity, boundedness, symplectic maps, conservative maps, Liouville theorem.

• Network Theory

Keywords: Complex networks, network efficiency, network vulnerability,  network optimization, network topology, network design, random networks, small-world networks, scale-free networks, graph theory, evolving networks, network tolerance, error tolerance, attack tolerance, network connectivity, biological networks, information networks.

• Other topics

In addition, I have published a collection of miscellaneous works in other fields, including: Quantum Mechanics, Cosmology, Fractals, Physics Teaching, Mathematics Teaching, Statistics and History of Science.

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SOME LINKS

      These are some groups important in my scientific and academic life: