Permanence of nonautonomous ratio dependent predator prey systems with piecewise constant argument of generalized type

2008-01-01
Akhmet, Marat
Xıaoyan, Lıu
In this paper, we investigate the dynamics of nonautonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type (PCAG) [3]. Sufficient conditions are established for some related qualitative properties such as positive invariance, permanence and non-persistence of the systems. Keywords. Piecewise constant argument of generalized type, predator-prey systems, ratio-dependent response, permanence, non-persistence. AMS (MOS) subject classification: 34A36, 34K12, 34K25.
Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Suggestions

Impulsive Hopfield-type neural network system with piecewise constant argument
Akhmet, Marat; Yılmaz, Elanur (2010-08-01)
In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type
Akhmet, Marat; Yılmaz, Elanur (2010-09-01)
In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.
Stability of differential equations with piecewise constant arguments of generalized type
Akhmet, Marat (Elsevier BV, 2008-02-15)
In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367-383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and Sufficient conditions for stability of the zero Solution are ob...
Global exponential stability of neural networks with non-smooth and impact activations
Akhmet, Marat (2012-10-01)
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
THE COMPLEXITY OF THE TOPOLOGICAL CONJUGACY PROBLEM FOR TOEPLITZ SUBSHIFTS
Kaya, Burak (2017-06-01)
In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This result provides a partial answer to a question asked by Sabok and Tsankov.
Citation Formats
M. Akhmet and L. Xıaoyan, “Permanence of nonautonomous ratio dependent predator prey systems with piecewise constant argument of generalized type,” Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, pp. 37–51, 2008, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/77722.