In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these eq...

Low codimensional bifurcations of control systems have been classified using the theory of normal forms. However, the normal form theory was developed as local results. To understand the behavior of control systems outside a local area of a bifurcation point, it is necessary to study the convergence of the normal forms if the vector fields are analytic. The convergence is a long time open probl...

We consider control systems of the type ẋ = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown time-varying signal with values in [0, 1] satisfying a permanent excitation condition i.e., ∫ t+T t α ≥ μ for every t ≥ 0, with 0 < μ ≤ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T, μ) if the real part of th...

The bifurcation and chaos phenomenon which exist in power grid are threats to the stable operation of power grid and the safety of people and equipment. In order to eliminate the chaos phenomena in power grid, a kind of non-singular terminal sliding mode (NTSM) variable structure control method based on immune algorithm is put forward. The second-order model of grid chaotic oscillation is built...

We consider control systems of the type ẋ = Ax+α(t)bu, where u ∈ R, (A, b) is a controllable pair and α is an unknown time-varying signal with values in [0, 1] satisfying a persistent excitation condition i.e., ∫ t+T t α(s)ds ≥ μ for every t ≥ 0, with 0 < μ ≤ T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T, μ) if the eigenvalu...

We study a bifurcation problem for a system of two differential equations in implicit form. For each value of the parameter θ, the solution yields a pair of Nash equilibrium strategies in feedback form, for a non-cooperative differential game. When θ = 0, the second player has no power to influence the dynamics of the system, and his optimal strategy is myopic. The game thus reduces to an optim...

This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit. When the regular orbit is a limit cycle, we can determine its associated Poincaré return map in terms of the in...

A pendulum can be stabilised in its upright position by proportionalplus-derivative (PD) feedback control only if the latency in the control loop is smaller than a certain critical delay. This critical delay is determined by the presence of a fully symmetric triple-zero eigenvalue singularity, a bifurcation of codimension three. We investigate three possible modifications of the PD scheme with ...

We present a numerical framework to treat infinite time horizon spatially distributed optimal control problems via the associated canonical system derived by Pontryagin’s Maximum Principle. The basic idea is to consider the canonical system in two steps. First we perform a bifurcation analysis of canonical steady states using the continuation and bifurcation package pde2path, yielding a number ...