Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling

Survey of the Farm Management, Focusing on the Regional Difference and Cattle Farming in Burkina Faso

In Burkina Faso the history using of cattle as draft power for cultivation is not long. This study was conducted to investigate the farm management, focusing on the regional difference and the presence of cattle farming in the country. Interview was carried out on 30 farms from B Province in the Centre-West Region consisting of 8 non-cattle owners (BNs) and 22 cattle owners (BCs), and on 9 farms of cattle owners from H Province in the Haut-Bassins Region (HCs) in November 2013. The average household sizes of BNs, BCs and HCs were 16.5, 27.2 and 31.3, respectively. The ratios of BNs, BCs and HCs having income sources from livestock farming equivalent to or more than crop farming were 25, 50 and 67%, respectively. The average cattle number of BCs was 8.6 and that of HCs was 50.8. The average planted areas of BNs, BCs and HCs were 4.9, 12.0 and 7.0 ha, respectively. The BCs and BNs had large planted area of millet, rice, sorghum and peanut, on the other hand, planted area of maize, sesame seed, cotton and vegetables was large in HCs. The gross income from the crop farming of BNs and BCs were 95,000 and 114,000 FCFA/year, respectively, which were higher than that of HCs: 59,000 FCFA/year. The gross income and profit from cattle farming of HCs were twice and thrice as high as those of BCs, respectively. The ratio of the gross income from cattle farming to that from total farming of BCs and HCs were high, 72 and 80%, respectively. The results suggested that cattle farming contributed to the profit of farmers in B Province, who had a low profit margin of the crop and vegetable farming due to the constraints of soil condition and climate results from the limit of precipitation

Border Avoidance: Necessary Regularity for Coefficients and Viscosity Approach

Motivated by the result of invariance of regular-boundary open sets in \cite{CannarsaDaPratoFrankowska2009} and multi-stability issues in gene networks, our paper focuses on three closely related aims. First, we give a necessary local Lipschitz-like condition in order to expect invariance of open sets (for deterministic systems). Comments on optimality are provided via examples. Second, we provide a border avoidance (near-viability) counterpart of \cite{CannarsaDaPratoFrankowska2009} for controlled Brownian diffusions and piecewise deterministic switched Markov processes (PDsMP). We equally discuss to which extent Lipschitz-continuity of the driving coefficients is needed. Finally, by applying the theoretical result on PDsMP to Hasty's model of bacteriophage (\cite{hasty\_pradines\_dolnik\_collins\_00}, \cite{crudu\_debussche\_radulescu\_09}), we show the necessity of explicit modeling for the environmental cue triggering lysis

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

Invariance Conditions for Nonlinear Dynamical Systems

Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions, sufficient and necessary conditions, under which some convex sets are invariant sets for linear dynamical systems. In this paper, by utilizing analogous methodology, we generalize the results for nonlinear dynamical systems. First, the Theorems of Alternatives, i.e., the nonlinear Farkas lemma and the \emph{S}-lemma, together with Nagumo's Theorem are utilized to derive invariance conditions for discrete and continuous systems. Only standard assumptions are needed to establish invariance of broadly used convex sets, including polyhedral and ellipsoidal sets. Second, we establish an optimization framework to computationally verify the derived invariance conditions. Finally, we derive analogous invariance conditions without any conditions

Effect Of Planting Device And Seed Sorting On Yield Of Maize

ABSTRACT: Experiments were conducted at the CSIR-Crops Research Experimental station at Kumasi, Ghana, to determine the effects of seed sorting and planting device on yield of maize in the 2014 major growing season. Two jab planters were used to plant sorted and unsorted seeds. The control treatment was cutlass planting of unsorted seed. One of the jab planters was imported from China; and the other was fabricated in Ghana. The experimental design was a randomized complete block with 3 replications. Planting one hectare of maize with the Chinese planter took about 10 hours, 36 minutes; the local planter took 12 hours 39 minutes, whilst cutlass took 29 hours 36 minutes. Seed sorting and planting device had no significant effect on maize yield. However it was faster, cheaper and economically more viable to plant with jab planter than with cutlass

Nanoparticle synthesis using high-powered pulse-modulated induction thermal plasma

金沢大学理工研究域電子情報学系Nanoparticle synthesis was performed using the high-powered pulse-modulated induction thermal plasma (PMITP) technique to study the effect of coil current modulation on synthesized nanoparticles. This is the first paper to present a summary of results of TiO2 nanoparticle synthesis using high-power Ar-O2 PMITP at 20 kW. The synthesized particles were analysed using field emission scanning electron microscopy and X-ray diffractometry. In addition, optical emission spectroscopy was used during nanoparticle synthesis experiments to measure TiO spectra and to determine the time-averaged vibrational and rotational temperatures of TiO in the reaction chamber. The results showed that the PMITP produced smaller nanoparticles and a narrower size distribution of particles. Moreover, PMITP provided a lower temperature region in the reaction chamber downstream of the plasma torch than such regions in non-modulated thermal plasmas. © 2010 IOP Publishing Ltd

Noise Induced Coherence in Neural Networks

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in the thermodynamic limit ($N\to \infty$) a broadband peak and an additional delta-function peak that is absent from the powerspectrum of an isolated element. The powerspectrum of the mean output signal only exhibits the delta-function peak. These results are explained analytically in an exactly soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure

Mapping degree in Banach spaces and spectral theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46287/1/209_2005_Article_BF01187933.pd