Stability and bifurcation analysis of Westwood+ TCP congestion control model in mobile cloud computing networks

In this paper, we first build up a Westwood+ TCP congestion control model with communication delay in mobile cloud computing networks. We then study the dynamics of this model by analyzing the distribution ranges of eigenvalues of its characteristic equation. Taking communication delay as the bifurcation parameter, we derive the linear stability criteria depending on communication delay. Furthermore, we study the direction of Hopf bifurcation as well as the stability of periodic solution for the Westwood+ TCP congestion control model with communication delay. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by the normal form theory and the center manifold theorem. Finally, numerical simulation is done to verify the theoretical results

An information diffusion model in social networks with carrier compartment and delay

With the wide applications of the communication networks, the topic of information networks security is getting more and more attention from governments and individuals. This paper is devoted to investigating a malware propagation model with carrier compartment and delay to describe the process of malware propagation in mobile wireless sensor networks. Based on matrix theory for characteristic values, the local stability criterion of equilibrium points is established. Applying the linear approximation method of nonlinear systems, we study the existence of Hopf bifurcation at the equilibrium points. At the same time, we identify some sensitive parameters in the process of malware propagation. Finally, numerical simulations are performed to illustrate the theoretical results

bifurcation analysis of a delayed worm propagation model with saturated incidence

This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results

Stability and bifurcation analysis of multi-element non-foster networks

A stability and bifurcation analysis of multi-element non-Foster networks is presented, illustrated through its application to non-Foster transmission lines. These are obtained by periodically loading a passive transmission line with negative capacitors, implemented with negative-impedance converters (NICs). The methodology takes advantage of the possibility to perform a stability analysis per subintervals of the perturbation frequency. This will allow an independent analytical study of the low-frequency instability, from which simple mathematical criteria will be derived to prevent bias-network instabilities at the design stage. Then, a general numerical method, based on a combination of the Nyquist criterion with a pole-zero identification of the individual NIC, will be presented, which will enable the detection of both low- and high-frequency instabilities. A bifurcation analysis of the multi-element non-Foster structure will also be carried out, deriving the bifurcation condition from a matrix-form formulation of the multi-element structure. The judicious choice of the observation ports will enable a direct calculation of all the coexisting bifurcation loci, with no need for continuation procedures. These bifurcation loci will provide useful insight into the global-stability properties of the whole NIC-loaded structure.This work was supported in part by the Spanish Ministry of Economy and Competitiveness and in part by the European Regional Development Fund (ERDF/FEDER) under Project TEC2014-60283-C3-1-R and Project TEC2017-88242-C3-1-R

Hysteresis and oscillation in high-efficiency power amplifiers

Hysteresis in power amplifiers (PAs) is investigated in detail with the aid of an efficient analysis method, compatible with commercial harmonic balance. Suppressing the input source and using, instead, an outer-tier auxiliary generator, together with the Norton equivalent of the input network, analysis difficulties associated with turning points are avoided. The turning-point locus in the plane defined by any two relevant analysis parameters is obtained in a straightforward manner using a geometrical condition. The hysteresis phenomenon is demonstrated to be due to a nonlinear resonance of the device input capacitance under near optimum matching conditions. When increasing the drain bias voltage, some points of the locus degenerate into a large-signal oscillation that cannot be detected with a stability analysis of the dc solution. In driven conditions, the oscillation will be extinguished either through synchronization or inverse Hopf bifurcations in the upper section of the multivalued curves. For an efficient stability analysis, the outer-tier method will be applied in combination with pole-zero identification and Hopf-bifurcation detection. Departing from the detected oscillation, a slight variation of the input network will be carried out so as to obtain a high-efficiency oscillator able to start up from the noise level. All the tests have been carried out in a Class-E GaN PA with measured 86.8% power-added efficiency and 12.4-W output power at 0.9 GHz.This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under Project TEC2014-60283-C3-1-R and Project TEC2014-58341-C4-1-R, with FEDER co-funding, the Parliament of Cantabria (12.JP02.64069) and by the Predoctoral Fellowship for Researchers in Training of the University of Cantabria and the Regional Ministry of Education of the Government of Cantabria

Efficient simulation of solution curves and bifurcation loci in injection-locked oscillators

A new method is presented for the two-level harmonic-balance analysis of multivalued synchronized solution curves in injection-locked oscillators. The method is based on the extraction of a nonlinear admittance function, which describes the circuit response from the input source terminals. It does not require any optimization or parameter switching procedures, this constituting a significant advantage compared with previous analysis techniques. With additional mathematical conditions, it enables a straightforward determination of the turning point and Hopf bifurcation loci that delimit the stable injection-locked operation bands. The codimension two bifurcation point at which the turning point and Hopf bifurcation loci merge is analyzed in detail, as well as the saddle-connection locus. As it is shown, a second intersection of the saddle-connection locus with the turning point locus acts as a boundary between synchronization points and points associated with jumps and hysteresis. The likely observation of chaotic solutions in the neighborhood of the saddle-connection locus is discussed too. The techniques have been validated by application to several injection-locked oscillators, obtaining good agreement with the experimental results.This work was supported by the Spanish Ministry of Economy and competitiveness under contract TEC2011-29264-C03-01 and the predoctoral fellowship for researchers in training of the University of Cantabria and the Regional Ministry of Education of the Government of Cantabria