In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = f(n− 1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p gcd(p,k) periodic...

*Correspondence: [email protected] 1Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract The basic reproductive number R0 of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asympto...

We propose and analyze an age-structured partial differential model for hematopoietic stem cell dynamics, in which proliferation, differentiation and apoptosis are regulated by growth factor concentrations. By integrating the age-structured system over the age and using the characteristics method, we reduce it to a delay differential system. We investigate the existence and stability of the ste...

The paper presents the role of self-stabilization analysis in the design, verification and validation of the dynamics of an Adaptive Flight Control System (AFCS). Since the traditional self-stabilization approaches lack the flexibility to deal with the continuous adaptation of the neural network within the AFCS, the paper emphasizes an alternate self-stability analysis approach, namely Lyapunov...

In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that “multiple Lyapunov functions” are commonly used in the stability theory for hybrid systems. We will show that the e...

We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4(+) T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replicatio...

A data-driven identification of dynamical systems requiring only minimal prior knowledge is promising whenever no analytically derived model structure is available, e.g., from first principles in physics. However, meta-knowledge on the system’s behavior is often given and should be exploited: Stability as fundamental property is essential when the model is used for controller design or movement...

Abstract: In this paper, a decentralized control problem is considered for multimachine power systems with nonlinear interconnections and disturbances. A direct feedback linearization compensator is employed to cancel most of the nonlinearities, and then a backstepping procedure is applied to deal with the interconnections and to reduce the effects of a disturbance that does not satisfy the mat...

In this paper, we present results on the implementation of a hierarchical quaternion based attitude and trajectory controller for manual and autonomous flights of quadrotors. Unlike previous papers on using quaternion representation, we use the nonlinear complementary filter that estimates the attitude in quaternions and as such does not involve Euler angles or rotation matrices. We show that f...