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This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.

Limit properties of solutions of singular second-order differential equations.

Rachůnková, Irena, Staněk, Svatoslav, Weinmüller, Ewa, Zenz, Michael (2009)

Boundary Value Problems [electronic only]

Limits of solutions of a perturbed linear differential equation.

Avramescu, Cezar, Vladimirescu, Cristian (2002)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Linear impulsive dynamic systems on time scales.

Lupulescu, Vasile, Zada, Akbar (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Linear perturbations of a constant coefficient differential equation subject to mild integral smallness conditions

William F. Trench (1986)

Czechoslovak Mathematical Journal

Linear Stability of Fractional Reaction - Diffusion Systems

Y. Nec, A. A. Nepomnyashchy (2010)

Mathematical Modelling of Natural Phenomena

Theoretical framework for linear stability of an anomalous sub-diffusive activator-inhibitor system is set. Generalized Turing instability conditions are found to depend on anomaly exponents of various species. In addition to monotonous instability, known from normal diffusion, in an anomalous system oscillatory modes emerge. For equal anomaly exponents for both species the type of unstable modes is determined by the ratio of the reactants' diffusion coefficients. When the ratio exceeds its normal...

Linear stability theory of solitary waves arising from Hamiltonian systems with symmetry

Stubbe, Joachim (1989)

Portugaliae mathematica

Linear uncertain non-autonomous time-delay systems: Stability and stabilizability via Riccati equations.

Niamsup, Piyapong, Mukdasai, Kanit, Phat, Vu N. (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Linearized stability results in continuous interpolation spaces

A. Schiaffino, A. Tesei (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Local and global properties of nonautonomous dynamical systems and their application to competition models.

Il'ichev, V.G. (2003)

Sibirskij Matematicheskij Zhurnal

Local asymptotic stability for nonlinear quadratic functional integral equations.

Dhage, B.C., Bellale, S.S. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli (2009)

Serdica Journal of Computing

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.We consider a nonlinear model of a continuously stirred bioreactor and study the stability of the equilibrium points with respect to practically important model parameters. We determine regions in the parameter space where the steady states undergo transcritical and Hopf bifurcations. In the latter case, the stability of the emerged limit cycles is also studied. Numerical simulations in the computer algebra...

Local method of nonlinear analysis

A. D. Bruno (1988)

Banach Center Publications

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