We consider a difference equation involving three parameters and a piecewise constant control function with an additional positive threshold λ. Treating the threshold as a bifurcation parameter that varies between 0 and∞, we work out a complete asymptotic and bifurcation analysis. Among other things, we show that all solutions either tend to a limit 1-cycle or to a limit 2-cycle and, we find th...

Abstract: We propose a new approach to the study of Nash equilibrium solutions to non-cooperative differential games. The original problem is embedded in a one-parameter family of differential games, where the parameter θ ∈ [0, 1] accounts for the strength of the second player. When θ = 0, the second player adopts a myopic strategy and the game reduces to an optimal control problem for the firs...

In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...

We derive analytical expressions of codim-1-bifurcations for a fully connected, additive two-neuron network with sigmoidal activations, where the two external inputs are regarded as bifurcation parameters. The obtained NeimarkSacker bifurcation curve encloses a region in input space with stable oscillatory behaviour, in which it is possible to control the oscillation frequency by adjusting the ...

‎in this paper‎, ‎first we discuss a local stability analysis of model was introduced by p‎. ‎j‎. ‎mumby et‎. ‎al‎. ‎(2007)‎, ‎with $frac{gm^{2}}{m+t}$ as the functional response term‎. ‎we conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef‎. ‎next‎, ‎we consider this model under the influence of the time delay as the bifurcat...

In Canada the number of West Nile virus (WNv) infection of humans decreasing during the years of 2007-2010. However, it started increasing once more during last year 2011 despite the immense efforts exhibited by the specialized agencies to control the vector mosquitoes and the disease. In this study, we use mathematical models to study the behavior of the transmission of WNv in the mosquito-bir...

Cerebral aneurysms are thought to develop at locations of hemodynamic shear stress, via an inflammatory process. The molecular mechanism that links shear stress to inflammation, however, is not completely understood. Progress in studying this disease is limited by a lack of a suitable in vitro model. To address this, we designed novel in vitro parallel-plate flow chamber models of a straight ar...

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...

This study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos. A phase portrait, maximum Lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro-electro-mechanical system (MEMS). To suppress chaotic motion, a robust fuzzy sliding mode controller (FSMC) is designed to tur...