here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

comnode classification within membrane residue curves (m-rcms) currently hinges on lyapunov’s theorem and therefore the computation of mathematically complex eigenvalues. this paper presents an alternative criterion for the classification of nodes within m-rcms based on the total membrane flux at node compositions. this paper demonstrates that for a system exhibiting simple permeation behaviour...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov fun...

The Lyapunovmethod for stability analysis of an equilibrium state of a nonlinear dynamic system requires a Lyapunov function v(t, x) having the following properties: (1) v is a positive definite function, and (2) v̇ is at least a negative semi-definite function. Finding such a function is a challenging task. The first theorem presented in this paper simplifies the second property for a Lyapunov ...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete–time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi–global practical Lyapunov functions for globally asymptotica...