Supratransmission phenomenon in a Fermi-Pasta-Ulam diatomic lattice.

The nonlinear supratransmission phenomenon in a Fermi-Pasta-Ulam (FPU) diatomic lattice with two forbidden bands is investigated. Using a decoupling ansatz for the motion of the two different sublattices combined with the continuum (quasidiscrete) approximation, we derived analytically the threshold amplitudes of supratransmission occurrence when a sinusoidal driving with frequency in the upper forbidden band (lower forbidden band gap between acoustic and optical modes) is applied at one end. The resulting estimate of the threshold of a lattice with a first heavy particle is different to the one obtained from a lattice with a first light particle, showing the influence of the driven particle and giving also the possibility to have two thresholds on each forbidden gap of a diatomic lattice by switching the order of light (m) and heavy (M) masses. In the lower forbidden band, the dependence of the supratransmission threshold on the mass ratio (µ=m/M) has been evidenced and it appears that for large (small) values of µ, that is µ>60%, the coupling between the two modes must (must not) be considered. Numerical explorations were subsequently performed with an emphasis on the dependence of the threshold on the driving frequency and also on the mass of the driven particle (light or heavy). A good agreement is found between the numerical and analytical thresholds. For the limit case where all the masses are identical, the results of the monoatomic FPU previously found in the literature are recovered.

Diversity-enhanced stability.

We give compelling evidence that diversity, represented by a quenched disorder, can produce a resonant collective transition between two unsteady states in a network of coupled oscillators. The stability of a metastable state is optimized and the mean first-passage time maximized at an intermediate value of diversity. This finding shows that a system can benefit from inherent heterogeneity by allowing it to maximize the transition time from one state to another at the appropriate degree of heterogeneity.

Enhanced signal response in globally coupled networks of bistable oscillators: Effects of mean field density and signal shape.

This paper studies a set of globally coupled bistable oscillators, all subjected to the same weak periodic signal and identical coupling. The effect of mean field density (MFD) on global dynamics is analyzed. The oscillators switch from intra- to interwell motion as MFD increases, clearly demonstrating MFD-enhanced signal amplification. A maximum amplification also occurs at a moderate level of MFD, indicating that the response exhibits a nonmonotonic sensitivity to MFD. The MFD-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. The analytical investigation provides a simplified model to study the mechanism underlying this resonancelike behavior. It is shown that by modifying the bistability nature of the potential energy, the mean field density can promote well-to-well oscillations and larger amplitude motions. Finally, the robustness of this phenomenon to various signal waveforms is examined. It can therefore be used alternatively to efficiently amplify weak signals in practical situations with large network sizes.

Using coupling imperfection to control amplitude death.

Previous studies of nonlinear oscillator networks have shown that amplitude death (AD) occurs after tuning oscillator parameters and coupling properties. Here, we identify regimes where the opposite occurs and show that a local defect (or impurity) in network connectivity leads to AD suppression in situations where identically coupled oscillators cannot. The critical impurity strength value leading to oscillation restoration is an explicit function of network size and system parameters. In contrast to homogeneous coupling, network size plays a crucial role in reducing this critical value. This behavior can be traced back to the steady-state destabilization through a Hopf's bifurcation, which occurs for impurity strengths below this threshold. This effect is illustrated across different mean-field coupled networks and is supported by simulations and theoretical analysis. Since local inhomogeneities are ubiquitous and often unavoidable, such imperfections can be an unexpected source of oscillation control.

Malaria metrics distribution under global warming: assessment of the VECTRI malaria model over Cameroon.

Malaria is a critical health issue across the world and especially in Africa. Studies based on dynamical models helped to understand inter-linkages between this illness and climate. In this study, we evaluated the ability of the VECTRI community vector malaria model to simulate the spread of malaria in Cameroon using rainfall and temperature data from FEWS-ARC2 and ERA-interim, respectively. In addition, we simulated the model using five results of the dynamical downscaling of the regional climate model RCA4 within two time frames named near future (2035-2065) and far future (2071-2100), aiming to explore the potential effects of global warming on the malaria propagation over Cameroon. The evaluated metrics include the risk maps of the entomological inoculation rate (EIR) and the parasite ratio (PR). During the historical period (1985-2005), the model satisfactorily reproduces the observed PR and EIR. Results of projections reveal that under global warming, heterogeneous changes feature the study area, with localized increases or decreases in PR and EIR. As the level of radiative forcing increases (from 2.6 to 8.5 W.m-2), the magnitude of change in PR and EIR also gradually intensifies. The occurrence of transmission peaks is projected in the temperature range of 26-28 °C. Moreover, PR and EIR vary depending on the three agro-climatic regions of the study area. VECTRI still needs to integrate other aspects of disease transmission, such as population mobility and intervention strategies, in order to be more relevant to support actions of decision-makers and policy makers.

Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape.

The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.

The effect of climate variability in the efficacy of the entomopathogenic fungus Metarhizium acridum against the desert locust Schistocerca gregaria.

Despite substantial efforts to control locusts they remain periodically a major burden in Africa, causing severe yield loss and hence loss of food and income. Distribution maps indicating the value of the basic reproduction number R0 was used to identify areas where an insect pest can be controlled by a natural enemy. A dynamic process-based mathematical model integrating essential features of a natural enemy and its interaction with the pest is used to generate R0 risk maps for insect pest outbreaks, using desert locust and the entomopathogenic fungus Metarhizium acridum (Synn. Metarhizium anisoliae var. acridum) as a case study. This approach provides a tool for evaluating the impact of climatic variables such as temperature and relative humidity and mapping spatial variability on the efficacy of M. acridum as a biocontrol agent against desert locust invasion in Africa. Applications of M. acridum against desert locust in a few selected African countries including Morocco, Kenya, Mali, and Mauritania through monthly spatial projection of R0 maps for the prevailing climatic condition are illustrated. By combining mathematical modeling with a geographic information system in a spatiotemporal projection as we do in this study, the field implementation of microbial control against locust in an integrated pest management system may be improved. Finally, the practical utility of this model provides insights that may improve the timing of pesticide application in a selected area where efficacy is highly expected.

Understanding biological control with entomopathogenic fungi-Insights from a stochastic pest-pathogen model.

In this study, an individual-based model is proposed to investigate the effect of demographic stochasticity on biological control using entomopathogenic fungi. The model is formulated as a continuous time Markov process, which is then decomposed into a deterministic dynamics using stochastic corrections and system size expansion. The stability and bifurcation analysis shows that the system dynamic is strongly affected by the contagion rate and the basic reproduction number. However, sensitivity analysis of the extinction probability shows that the persistence of a biological control agent depends to the proportion of spores collected from insect cadavers as well as their ability to be reactivated and infect insects. When considering the migration of each species within a set of patches, the dispersion relation shows a Hopf-damped Turing mode for a threshold contagion rate. A large size population led to a spatial and temporal resonant stochasticity and also induces an amplification effect on power spectrum density.

Collective escape and supratransmission phenomena in a nonlinear oscillators chain.

In this study, the collective escape and supratransmission phenomena along a nonlinear chain of coupled particles subjected to a cubic on-site potential are considered. It is shown that the minimum initial on-site amplitude for which there is a collective escape increases with the nonlinear coupling. When the chain is forced at one end by a periodical excitation, the system exhibits supratransmission phenomenon in both lower and upper forbidden bandgaps, and, subsequently, it appears that the driving amplitude threshold for supratransmission in the upper forbidden bandgap frequency decreases with the nonlinear coupling. Depending on the frequency range of the gap frequency, the collective escape and supratransmission can occur simultaneously; otherwise, the supratransmission prevails.

Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions.

The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schrödinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.

Modelled and observed mean and seasonal relationships between climate, population density and malaria indicators in Cameroon.

BACKGROUND: A major health burden in Cameroon is malaria, a disease that is sensitive to climate, environment and socio-economic conditions, but whose precise relationship with these drivers is still uncertain. An improved understanding of the relationship between the disease and its drivers, and the ability to represent these relationships in dynamic disease models, would allow such models to contribute to health mitigation and adaptation planning. This work collects surveys of malaria parasite ratio and entomological inoculation rate and examines their relationship with temperature, rainfall, population density in Cameroon and uses this analysis to evaluate a climate sensitive mathematical model of malaria transmission. METHODS: Co-located, climate and population data is compared to the results of 103 surveys of parasite ratio (PR) covering 18,011 people in Cameroon. A limited set of campaigns which collected year-long field-surveys of the entomological inoculation rate (EIR) are examined to determine the seasonality of disease transmission, three of the study locations are close to the Sanaga and Mefou rivers while others are not close to any permanent water feature. Climate-driven simulations of the VECTRI malaria model are evaluated with this analysis. RESULTS: The analysis of the model results shows the PR peaking at temperatures of approximately 22 °C to 26 °C, in line with recent work that has suggested a cooler peak temperature relative to the established literature, and at precipitation rates at 7 mm day-1, somewhat higher than earlier estimates. The malaria model is able to reproduce this broad behaviour, although the peak occurs at slightly higher temperatures than observed, while the PR peaks at a much lower rainfall rate of 2 mm day-1. Transmission tends to be high in rural and peri-urban relative to urban centres in both model and observations, although the model is oversensitive to population which could be due to the neglect of population movements, and differences in hydrological conditions, housing quality and access to healthcare. The EIR follows the seasonal rainfall with a lag of 1 to 2 months, and is well reproduced by the model, while in three locations near permanent rivers the annual cycle of malaria transmission is out of phase with rainfall and the model fails. CONCLUSION: Malaria prevalence is maximum at temperatures of 24 to 26 °C in Cameroon and rainfall rates of approximately 4 to 6 mm day-1. The broad relationships are reproduced in a malaria model although prevalence is highest at a lower rainfall maximum of 2 mm day-1. In locations far from water bodies malaria transmission seasonality closely follows that of rainfall with a lag of 1 to 2 months, also reproduced by the model, but in locations close to a seasonal river the seasonality of malaria transmission is reversed due to pooling in the transmission to the dry season, which the model fails to capture.

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity.

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.

Theoretical analysis of spatial nonhomogeneous patterns of entomopathogenic fungi growth on insect pest.

This paper presents the study of the dynamics of intrahost (insect pests)-pathogen [entomopathogenic fungi (EPF)] interactions. The interaction between the resources from the insect pest and the mycelia of EPF is represented by the Holling and Powell type II functional responses. Because the EPF's growth is related to the instability of the steady state solution of our system, particular attention is given to the stability analysis of this steady state. Initially, the stability of the steady state is investigated without taking into account diffusion and by considering the behavior of the system around its equilibrium states. In addition, considering small perturbation of the stable singular point due to nonlinear diffusion, the conditions for Turing instability occurrence are deduced. It is observed that the absence of the regeneration feature of insect resources prevents the occurrence of such phenomena. The long time evolution of our system enables us to observe both spot and stripe patterns. Moreover, when the diffusion of mycelia is slightly modulated by a weak periodic perturbation, the Floquet theory and numerical simulations allow us to derive the conditions in which diffusion driven instabilities can occur. The relevance of the obtained results is further discussed in the perspective of biological insect pest control.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy.

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.

Waves transmission and amplification in an electrical model of microtubules.

Inspired by standard electrophysiological models of microtubules, a discrete nonlinear equation for ionic wave propagation that incorporates a negative nonlinear resistance is presented. The conditions for wave propagation in forbidden band gap are analyzed without and with dissipation. The nonlinear response manifold method is used to determine the supratransmission threshold of the case of study without dissipation. This threshold is found to be similar to the value obtained by analytical methods. With the dissipation, the monitoring of the accumulated energy is used to estimate the infratransmission threshold. It appears that the value of the supratransmission threshold can be lower than the value of the infratransmission threshold. The system is found to amplify significantly the amplitude of the input signal, thus confirming known experimental results. Nevertheless, a proper choice of the parameter of the nonlinear resistance is required for further validation of our results. A possible biological implication of the obtained results is presented.

Controlled synchronization of chaotic systems with uncertainties via a sliding mode control design.

This paper addresses the problem of robust adaptive control for synchronization of continuous-time coupled chaotic systems with uncertainties. A general model is studied using measured output state feedback control. An adaptive controller is designed based on a sliding mode control design. When only the output variable is measurable for synchronization, the adaptive controller is designed by incorporating with an observer. Two numerical examples are presented to show the effectiveness of the proposed chaos synchronization method.