In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate local global stability steady-states. deduce basic reproductive threshold parameter, so that if R0<1, disease-free steady-state is locally globally asymptotically stable. However, for R0>1, there exists positive (endemic) which A Hollin...

In this paper we consider the global and local stability and instability of solutions of a scalar nonlinear differential equation with non–negative solutions. The differential equation is a perturbed version of a globally stable autonomous equation with unique zero equilibrium where the perturbation is additive and independent of the state. It is assumed that the restoring force is asymptotical...

Given a globally asymptotically controllable system, we derive from an existence theorem of a semiconcave control-Lyapunov function, the construction of a globally asymptotically stable feedback in the Euler sense. The feedback is rather regular in the case of control systems affine in the control. Abridged English Version In this paper, we study systems of the general form ẋ(t) = f(x(t), u(t))...

The transmission dynamics of a pertussis-pneumonia co-infection model is analyzed. takes into account temporary immunity infected infants and includes maternally derived compartment. basic reproduction number the co-infected obtained using next generation matrix, stability analysis carried out. exhibits four equilibria, namely, pertussis-free equilibrium, pneumonia-free co-infection-free equili...

We study multi-pulse solutions in excitable media. Under the assumption that a single pulse is asymptotically stable, we show that there is a well-defined ”shooting manifold”, consisting of two pulses traveling towards each other. In the phase space, the two-dimensional manifold is a graph over the manifold of linear superpositions of two pulses located at x1 and x2, with x1 − x2 1. It is local...

In this paper, we derive a result for stabilizability and a separation principle for periodic orbits. First, using degree theory, we derive a necessary condition for local asymptotic stabilizability of periodic orbits. This condition is similar to the famous Brockett’s necessary condition (1983) for local asymptotic stabilizability for equilibria. Next, we derive a separation principle for peri...

The presence of the power-law memory is a significant feature many natural (biological, physical, etc.) and social systems. Continuous discrete fractional calculus instrument to describe behavior systems with memory. Existence chaotic solutions an intrinsic property nonlinear dynamics (regular fractional). Behavior can be very different from corresponding no Finding periodic points essential fo...