asymptotic stability

Mathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics

The purpose of this research is to suggest and analyze a spatiotemporal of an IS-LM model with two delays, interest rate, liquidity preference and general investment function.  The first delay into the proposed model refers to the time delay between the decision of investment and his implementation.  However, the second one represents the delay in investment production.  The well posedness of the model is proved.  The stability analysis and the existence of Hopf bifurcation are obtained.  Furthermore, numerical examples that confirm the analytical results are shown.

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

The dynamics of prey–predator interactions are often modeled using differential or difference equations.  In this paper, we investigate the dynamical behavior of a two-dimensional discrete prey–predator system.  The model is formulated in terms of difference equations and derived by using a nonstandard finite difference scheme (NSFD), which takes into consideration the non-overlapping generations.  The existence of fixed points as well as their local asymptotic stability are proved.  Further, it is shown that the model experiences Neimark–Sacker bifurcation (NSB for sho

Optimization of parametric balanced modulator based on frequency symbolic method

Application of the frequency symbolic method for analysis of established modes of linear periodically time-variable (LPTV) circuits to solving an optimization task conditioned by the control of their asymptotic stability is considered. The results of optimization of a parametric balanced modulator with respect to the criterion which is based on calculation of the parametric transfer functions approximated by Fourier trigonometric polynomials are presented.

Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems

The positivity and asymptotic stability of discrete-time and continuous-time nonlinear systems are addressed. Sufficient conditions for the positivity and asymptotic stability of the nonlinear systems are established. The proposed stability tests are based on an extension of the Lyapunov method to the positive nonlinear systems. The effectiveness of the tests are demonstrated on examples.