Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

On stability of differential equations with piecewise constant argument and the associated discrete equations using dichotomic map

Dichotomic maps are considered by means of the stability of the null solution of a class of differential equations with piecewise constant argument via associated discrete equations. Copyright © 2008 Watam Press.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Stability of the null solution of the equation ẋ(t) = -a(t)x(t) + b(t)x([t])

The asymptotic stability of the null solution of the equation ẋ(t) = -a(t)x(t)+b(t)x([t]) with argument [t], where [t] designates the greatest integer function, is studied by means of dichotomic maps. © 2010 Academic Publications.

Optimal and sub-optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright (C) 2001 John Wiley & Sons, Ltd.

Piecewise Linear Systems with Closed Sliding Poly-Trajectories

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fertility life table of Trichogramma pretiosum and Trichogramma acacioi (Hymenoptera : Trichogrammatidae) on Sitotroga cerealella (Lepidoptera : Gelechiidae) eggs at different constant temperatures

Fertility life tables were developed for both Trichogramma pretiosum and Trichogramma acacioi reared on Sitotroga cerealella eggs as an alternative host at five different temperatures. The egg parasitoids were first collected from Nipteria panacea eggs, a lepidopterous pest of avocado. Egg parasitoid females were individualized in small glass vials along with 40 eggs of the host during 24 h for parasitization. For evaluation of the parasitism capacity, a similar procedure was adopted, but cardboards with eggs were replaced every day. The net reproductive rate (Ro), intrinsic rate of increase (rm), finite rate of increase (lambda), and mean generation time (T) were estimated. Temperature affected all parameters for both Trichogramma species. The highest fecundity for both species was observed at 25degreesC. Extreme temperatures such as 15degreesC or 35degreesC negatively affect the development rate of both species.

Application of the Potentiometric Stripping Analysis with Constant Current for the Determination of Lithium Ions Using a Spinel-Type Manganese (IV) Oxide-Modified Carbon Paste Electrode

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-branes with variable tension model and the effective Newtonian constant

It is shown that, in the two brane time variation model framework, if the hidden brane tension varies according to the phenomenological Eotvos law, the visible brane tension behavior is such that its time derivative is negative in the past and positive after a specific time of cosmological evolution. This behavior is interpreted in terms of a useful mechanical system analog and its relation with the variation of the Newtonian (effective) gravitational constant is explored.

DC Electric Field Dependence of the Dielectric Constant of Pzt Thin Films Prepared by Polymeric Precursor Method

This work reports dielectric measurements performed on Pb(Zr0.53Ti0.47)O3 (PZT) thin films prepared by a polymeric precursor method. The -E curves obtained for the PZT film measured at 100 kHz, under a small ac 0.2 kV/cm signal-test and a dc scan featured a typical butterfly curve. However, the -E curves obtained for PZT film under a dc scan, with a scan rate of 0.003 V/s, shows a pronounced asymmetry. The absence of a symmetric secondary peak in -E curves could be an indication of essentially 180 domain switching.

Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Physiologic and productive responses of Holstein dairy cows with access to the constant or limited shade

The work: was carried out to evaluate the physiologic and productive responses of 16 Holstein breed cows, in different lactating stages and production levels, maintained in two free stall corral types, with or without plastic sheet covering, in the southeast-northwest of the covered area edges. The animals were confined in free stall system, during the months of the summer, with access to the constant or Limited shade. A complete randomized experimental design was: used. The physiological variables measured were respiratory frequency (morning an afternoon) and rectal temperature (morning and afternoon). The productive variables were milk production (morning, afternoon and daily), dry matter (DM) intake (% live weight) and efficiency of milk production (kg of milk/kg DM intake). The animals with access to the constant shade presented respiratory frequency (74.1 vs 81.0 breath/min.) and rectal temperature (39.5 vs 39.7 degrees C) lower and mirk production (22.6 vs 20.9 kg/day) and efficiency of milk production (1.3 vs 1.2 kg of milk/kg DM ingested) higher than the animals with access to the limited shade. There was no effect on the dry matter intake.