remarks on competitive coexistence the asymptotic behavior of two predators competing exploitatively for the same prey in a constant environment is analyzed in this paper assuming that the prey have fast dynamics it is proved through a singular perturbation argument that the two predators can coexist if the prey and predators parameters lie within specified ranges it is also shown that coexistence occurs through a simple periodic behavior a poor season characterized by an almost endemic presence of the prey alternates with a rich season during which prey are abundant and predators regenerate this property follows from the geometric nature of the equilibrium manifold and is therefore generic the results are in agreement with some conjectures supported by computer simulation and with the most recent theoretical findings on competitive coexistence

relative contributions of specific frequency bands to the loudness of broadband sounds listeners with normal hearing nh and sensorineural hearing loss snhl were asked to compare pairs of noise stimuli and choose the louder noise in each pair each noise was made up of 15 two erbn equivalent rectangular bandwidth wide frequency bands that varied independently over a 12 db range from one presentation to the next mean levels of the bands followed the long term average speech spectrum ltass or were set to 43 51 or 59 db sound pressure level spl the relative contribution of each band to the total loudness of the noise was determined by computing the correlation between the difference in levels for a given band on every trial and the listener s decision on that trial weights for snhl listeners were governed by audibility and the spectrum of the noise stimuli with bands near the spectral peak of the ltass noise receiving greatest weight nh listeners assigned greater weight to the lowest and highest bands an effect that increased with overall level but did not assign greater weight to bands near the ltass peak additional loudness matching and paired comparison studies using stimuli missing one of the 15 bands showed a significant contribution by the highest band but properties other than loudness may have contributed to the decisions

spectral shape discrimination by hearing impaired and normal hearing listeners the ability to discriminate between sounds with different spectral shapes was evaluated for normal hearing and hearing impaired listeners listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level in one condition the standard stimulus was the sum of six equal amplitude tones equal spl and in another the standard stimulus was the sum of six tones at equal sensation levels re audiometric thresholds for individual subjects equal sl spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation sensitivity was similar in all conditions for normal hearing and hearing impaired listeners the presence of perturbation and equal sl components increased thresholds for both groups but only small differences in weighting strategy were measured between the groups depending on whether the equal spl or equal sl condition was tested the average data suggest that normal hearing listeners may rely more on the central components of the spectrum whereas hearing impaired listeners may have been more likely to use the edges however individual weighting functions were quite variable especially for the hi listeners perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights such as internal noise or difficulty encoding a reference stimulus also may dominate performance

a method for proving the non existence of limit cycles abstract a general criterion is established for showing the non existence of periodic solutions and closed phase polygons of differential equations several known criteria of this type are obtained as special cases an extension is obtained for functional differential equations and several applications are given for specific special cases including homogeneous systems and population dynamics equations

detectability of increments and decrements in spectral profiles in auditory profile analysis the subject typically has to discriminate a standard spectrum consisting of widely spaced equal amplitude sinusoids from a comparison in which one or several components have been elevated relative to the others according to the widely accepted multichannel model however it should not matter whether the spectral shape alteration consists of incrementing or decrementing a component by a small number of decibels thus in order to investigate the generality of the hypothesized mechanism and to explore the role of pitch salience cues which might be thought to favor increments to single components two experiments comparing the detectability of intensity increments and decrements in spectral profiles were conducted in experiment 1 in which the number of components was varied from 3 to 15 within a fixed frequency range decrements to the central 800 hz component produced significantly larger thresholds than did increments experiment 2 which employed three tone complexes spanning different frequency ranges revealed that this effect is entirely due to the spectral density of the frequency components as the distance between the variable signal component and the flanking reference sinusoids decreased the increment decrement disparity became larger these effects may at least qualitatively be accounted for when peripheral excitation patterns are considered suggesting that local decrements are constrained more than increments by the excitation intruding from flanking stimulus components

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

on the finite amplitudes for open graphs in abelian dynamical colored boulatov ooguri models in the work ben geloun and bonzom 2011 int j theor phys 50 2819 it has been proved that the radiative corrections of the 2 point function in the su 2 boulatov tensor model generates a marginal in the renormalization group sense contribution of the form of a laplacian such a term which was missing in the initial boulatov model action should be added in that action before discussing the renormalization analysis of this model in this work by linearizing the group manifold we prove that the amplitudes associated with feynman graphs with external legs of the colored boulatov model over u 1 3 endowed with a laplacian dynamics are all convergent we conjecture that the same feature happens for the corresponding boulatov model over su 2 higher rank models are also discussed

the effect of enhanced spectral contrast on the internal representation of vowel shaped noise two steady state noise excited vowel sounds of 200 ms duration were synthesized one similar to a naturally produced whispered vowel the other with energy removed outside a nominal 50 hz band centered at each formant peak the threshold for a brief sinusoidal probe tone was measured at frequencies corresponding to the peaks and troughs in the vowel spectra in both forward and simultaneous masking the masking functions for a flat spectrum masker at each frequency were also measured so that the vowel masking patterns could be expressed in terms of the equivalent broadband masker level in the first experiment masking patterns for the two maskers were measured with three normal hearing subjects increasing spectral contrast was effective in increasing peak valley differences in the masking patterns up to 2 5 khz contrast was greater in forward than in simultaneous masking suggesting that the internal representation of a vowel may be enhanced by suppression in a second experiment masking patterns and flat spectrum masking functions were measured with three listeners with moderate sensorineural hearing impairments the enhancement produced by increasing spectral contrast was less than that obtained with normal hearing listeners but still present up to 2 5 khz a comparison of forward and simultaneous masking patterns again revealed an increase in peak valley differences suggesting that suppression mechanisms were still effective in these listeners the ability to enhance the internal representation of speechlike sounds in hearing impaired listeners may have implications for the design of signal processing hearing aids

spectral weights for overall level discrimination in listeners with sensorineural hearing loss a conditional on a single stimulus coss analysis procedure b g berg j acoust soc am 86 1743 1746 1989 was used to measure the weight or relative reliance that normal hearing and hearing impaired listeners give to different frequencies in the discrimination of the overall level of a multitone complex on each trial two multitone tone complexes comprised of six octave frequencies from 250 to 8000 hz were presented to subjects the levels of the frequencies for each complex were randomly varied the listeners task was to identify the complex with the higher overall intensity level normal hearing listeners used a variety of listening strategies to perform the task showing no general preference to weight one component over another hearing impaired listeners however showed a general tendency to give greatest weight to the spectral information in the region of their hearing loss thirteen of the 14 hearing impaired listeners all of whom had a high frequency sensorineural hearing loss weighted one or more of the high frequency components in the complex the greatest

a mathematical model of the chemostat with a general class of functions describing nutrient uptake a model of the chemostat involving n microorganisms competing for a single essential growth limiting substrate is considered instead of assuming the familiar michaelis menten kinetics for nutrient uptake a general class of functions is used which includes all monotone increasing uptake functions but which also allows uptake functions that describe inhibition by the substrate at high concentrations the qualitative behaviour of this generalized model is determined analytically it is shown that the behaviour depends intimately upon certain parameters provided that all the parameters are distinct which is a biologically reaonable assumption at most one competitor survives the substrate and the surviving competitor if one exists approach limiting values thus there is competitive exclusion however unlike the standard model in certain cases the outcome is initial condition dependent

stability and bifurcation analysis of a stage structured predator prey model with time delay abstract in this paper we proposed and analyzed a prey predator system with stage structured for the predator population a time delay is incorporated due to the gestation for the matured predator all the possible non negative equilibria are obtained and their local as well as global behavior are studied choosing delay as a bifurcation parameter the existence of the hopf bifurcation of the system has been investigated moreover we use the normal form method and the center manifold theorem to examine the direction of the hopf bifurcation and the nature of the bifurcating periodic solution some numerical simulations are given to support the analytical results some interesting conclusions are obtained from our analysis and it is given at the end of the paper

ward takahashi identities for the colored boulatov model ward takahashi wt identities of the colored boulatov model are derived using a generic unitary field transformation in a specific instance this generic transformation turns out to be a symmetry of the interaction so that particular classes of reduced wt identities for that symmetry are consequently identified and interpreted

different auditory filter bandwidth estimates based on profile analysis notched noise and hybrid tasks auditory filter bandwidths were estimated in three experiments the first experiment was a profile analysis experiment the stimuli were composed of sinusoidal components ranging in frequency from 200 to 5000 hz the standard stimulus was the sum of equal amplitude tones and the signal stimulus had a power spectrum that varied up down up down the number of components ranged from four to 60 interval by interval level randomization prevented the change in level of a single component from reliably indicating the change from standard to signal the second experiment was a notched noise experiment in which the 1000 hz tone to be detected was added to a noise with a notch arithmetically centered at 1000 hz detection thresholds were estimated both in the presence of and in the absence of level randomization in the third hybrid experiment a 1000 hz tone was to be detected and the masker was composed of equal amplitude sinusoidal components ranging in frequency from 200 to 5000 hz for this experiment thr

generalised conservation laws in non local field theories we propose a geometrical treatment of symmetries in non local field theories where the non locality is due to a lack of identification of field arguments in the action we show that the existence of a symmetry of the action leads to a generalized conservation law in which the usual conserved current acquires an additional non local correction term obtaining a generalization of the standard noether theorem we illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of bose einstein condensates we expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity

auditory profile analysis frequency phase and weber s law this paper reports three separate experiments on different aspects of performance in auditory profile analysis the first experiment deals with the effects of the frequency and position of an increment in a single component of a multitonal complex the general results indicate that detection of the signal is easier for components in the mid frequency range around 1000 hz independent of signal position within the complex the second experiment investigates the effects of relative phase of the individual components of the complex regardless of the number of components our results indicate that phase has very little effect even when different phases are selected for each presentation the third experiment compares the detection of an increment in intensity of a single component the traditional weber fraction experiment and conditions where additional components are present a profile experiment the detection of the increment is measured as a function of the level of the standard the single tone condition shows the usual near miss to weber s law whereas the multitone condition does not in addition threshold for the increment is better for the multitone condition than for the single tone condition for levels of the standard up to 70 db spl this last result is investigated for ten observers five of whom were experienced in profile tasks and five of whom were not using a low level standard the five experienced observers replicate the results described above the inexperienced observers show the opposite result on average they are better able to detect the increment in the single component condition

coexistence of a diffusive predator prey model with holling type ii functional response and density dependent mortality in this paper we consider a two competitor one prey diffusive model in which both competitors exhibit holling type ii functional response and one of the competitors exhibits density dependent mortality rate first we study the local and global existence of strong solution by using the c0 analytic semigroup then we consider the local and global stability of the positive constant equilibrium by using the linearization method and laypunov functional method respectively furthermore we derive some results for the existence and non existence of non constant stationary solutions when the diffusion rate of a certain species is small or large the existence of non constant stationary solutions implies the possibility of pattern formation in this system

zip bifurcation in a competition model on considere le systeme s s 1 s k m 1 x 1 s a 1 s m 2 x 2 s a 2 s x 1 m 1 x 1 s a 1 s d 1 w 1 x 2 m 2 x 2 s a 2 s d 2 x 2 soit i a i d i m i d i on etudie le cas 1 2

evaluation of simple models of auditory profile analysis using random reference spectra this article describes further study of the finding reported by green et al j acoust soc am 73 639 643 1983 and others that in certain conditions the threshold of detectability for an intensity increment to the center tone of a multitone reference spectrum decreased as the number of nonsignal tones increased that result was considered remarkable since critical band theory would predict that these nonsignal tones spaced outside the critical band containing the signal would have no effect on or at most slightly decrease within band detectability and certainly could not account for the result of improved detectability found in the study cited above recently henn and turner j acoust soc am 88 126 131 1990 were unable to replicate the result described above concluding that the phenomenon exists only in limited conditions and that it is highly individual in nature further they speculated that the most likely reason for the discrepancy between their study and previous s

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

global dynamics of a predator weaker prey and stronger prey system abstract in this paper we propose and analyze a prey predator system consisting of two competitive prey populations and one predator population which depends on both the prey species we investigate the boundedness and persistence criteria of the system and existence conditions of all the possible equilibria further the dynamical behavior from the point of view of local and global stability at different equilibria are presented we also determine the explicit conditions so that the system has no periodic solutions finally we present some numerical examples to illustrate our analytical works

spectral peak selection in spectral shape discrimination by normal hearing and hearing impaired listeners spectral shape discrimination thresholds were measured in the presence and absence of noise to determine whether normal hearing and hearing impaired listeners rely primarily on spectral peaks in the excitation pattern when discriminating between stimuli with different spectral shapes standard stimuli were the sum of 2 4 6 8 10 20 or 30 equal amplitude tones with frequencies fixed between 200 and 4000hz signal stimuli were generated by increasing and decreasing the levels of every other standard component the function relating the spectral shape discrimination threshold to the number of components n showed an initial decrease in threshold with increasing n and then an increase in threshold when the number of components reached 10 and 6 for normal hearing and hearing impaired listeners respectively the presence of a 50 db spl hz noise led to a 1 7db increase in threshold for normal hearing listeners and a 3 5db increase for hearing impaired listeners multichannel modeling and the relatively s

reduced frequency selectivity and the preservation of spectral contrast in noise reduced frequency selectivity associated with sensorineural hearing loss may pose particular problems for hearing impaired listeners in noisy environments in these situations broader than normal auditory filters may affect the perception of speech by reducing the contrast between spectral peaks and valleys in at least two ways first the peaks and valleys in the internal representation of the speech spectrum become smeared resulting in less precise frequency analysis second there may be a reduction in the signal to noise ratio s n at the output of each auditory filter in order to examine the relationship between frequency selectivity and identification of speechlike stimuli in noise hearing impaired and normal hearing listeners were trained to assign vowel labels to four harmonic complexes which differed in the frequency locations of four elevated peak harmonics peak harmonics were chosen to approximate first and second formant frequencies in four english vowels listeners were then tested to determine the spectral contrast necessary between peak and background components in order to maintain identification accuracy in the presence of various levels of broadband noise results indicated that for these stimuli normal hearing listeners required about 1 db of additional spectral contrast for every doubling of the intensity of noise the required increase in spectral contrast was generally greater for listeners with broader than normal auditory filters at 2000 hz this finding suggests indirectly that in the internal representations of speech sounds embedded in noise the signal to noise ratio for listeners with abnormal frequency selectivity is poorer than for listeners with normal frequency selectivity a poorer than normal internal s n may be one factor underlying the common observation that noise often is more degrading to speech understanding by hearing impaired listeners than by normal hearing listeners

periodic two predator one prey interactions and the time sharing of a resource niche a competition model involving two competing predator species and a single renewable resource prey species is studied under the assumption that the system parameters are periodic in time it is shown by means of global bifurcation techniques that a continuum of positive periodic solutions exists as a function of a selected averaged parameter and that the stability of these solutions at least locally near bifurcation depends on the direction of bifurcation in the special autonomous case of constant parameters the bifurcation is vertical and the spectrum of the continuum is a discrete point this autonomous case supports the principle of competitive exclusion in that coexistence of the predators on the single resource prey is possible in the sense that the system equilibrates only on a parameter set of measure zero in the more general case of periodic coefficients however it is shown that the spectrum can be an interval of positive length provided the predator parameter oscillations are out of phas

the number of components in profile analysis tasks the central issue of this paper is how detection of a change in spectral shape depends on the number of components m that define the spectrum first a channel theory is reviewed and the predictions relating the detectability of such a change as a function of the number of components are derived second the existing literature is reviewed most of it concerns the detection of an increment in a single tone of an m component equal amplitude complex the data are close 2 db to the predictions of the theory which suggests that there is a relatively small change in threshold as the number of components increases the consistency of the data is also discussed and hypotheses for discrepancies are presented finally the results of an experiment measuring the detectability of a special spectral shape change is explored in this case all the changes are equal in size but some are opposite in sign so that the summed change is zero the results using this balanced spectral change are also consistent with the predictions of the theory and show that for this special kind of spectral change thresholds improve by nearly 7 db as m increases from 4 to 24 components

finding nondegenerate hopf bifurcation points for four dimensional two parametric systems we establish a numerically feasible algorithm to find a simplicial approximation a to a certain part h41 of the boundary of the set h4 r4 of stable or hurwitz polynomials of degree 4 moreover we have that a hn using this we build an algorithm to find a piecewise linear approximation to the intersection curve of a given surface contained in r4 with h41 we have also devised an efficient computer program to perform all these operations the main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2 parametric hopf bifurcation problem of dimension 4

level discrimination of single tones in a multitone complex by normal hearing and hearing impaired listeners a conditional on a single stimulus coss analysis procedure j acoust soc am 86 1743 1746 1989 was used to estimate how well normal hearing and hearing impaired listeners selectively attend to individual spectral components of a broadband signal in a level discrimination task on each trial two multitone complexes consisting of six octave frequencies from 250 to 8000 hz were presented to listeners the levels of the individual tones were chosen independently and at random on each presentation the target tone was selected within a block of trials as the 250 1000 or 4000 hz component on each trial listeners were asked to indicate which of the two complex sounds contained the higher level target as a group normal hearing listeners exhibited greater selectivity than hearing impaired listeners to the 250 hz target while hearing impaired listeners showed greater selectivity than normal hearing listeners to the 4000 hz target which is in the region of their hearing loss both groups of listeners displayed large variability in their ability to selectively weight the 1000 hz target trial by trial analysis showed a decrease in weighting efficiency with increasing frequency for normal hearing listeners but a relatively constant weighting efficiency across frequency for hearing impaired listeners interestingly hearing impaired listeners selectively weighted the 4000 hz target which was in the region of their hearing loss more efficiently than did the normal hearing listeners

spectral weights in profile listening the coss analysis suggested by berg b g berg j acoust soc am 86 1743 1746 1989 is applied to a profile listening task the listener s task is to detect an increment in the level of the middle component of an n component spectrum the overall level of the components is randomly selected from a 20 db range on each presentation thus the detection task is essentially one of detecting a change in spectral shape to implement the coss analysis a small perturbation in level is added to each component of the complex coss functions are generated from these perturbations and the spectral weight that the listener assigns to each component is estimated data are reported for n 3 5 and 11 components and for perturbations with standard deviations of 0 5 1 and 2 db the estimated weights are similar to those derived for an optimum detector namely the level at the signal component is compared with the average level of the nonsignal components this result supports the view that profile analysis invol

hopf bifurcation in a two competitor one prey system with time delay in this paper we consider a delayed two competitor one prey system in which both two competitors exhibit holling ii functional response by choosing the time delay as a bifurcation parameter it is found that the hopf bifurcation occurs when the delay passes through a certain critical value numerical simulations are performed to illustrate the analytical results

permanence and extinction analysis for a delayed periodic predator prey system with holling type ii response function and diffusion abstract in this paper it is studied that two species predator prey lotka volterra type dispersal system with delay and holling type ii response function in which the prey species can disperse among n patches while the density independent predator species is confined to one of the patches and cannot disperse sufficient conditions of integrable form for the boundedness permanence extinction and the existence of positive periodic solution are established respectively

dynamic behaviour of a delayed predator prey model with harvesting abstract in this paper we analyze the dynamics of a delayed predator prey system in the presence of harvesting this is a modified version of the leslie gower and holling type ii scheme the main result is given in terms of local stability global stability influence of harvesting and bifurcation direction of hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem

sensitivity to changes in overall level and spectral shape an evaluation of a channel model two experiments involving level and spectral shape discrimination which test an optimal channel model developed by durlach et al j acoust soc am 80 63 72 1986 are described the model specifies how the auditory system compares and or combines intensity information in different frequency channels in the first experiment psychometric functions were obtained for the discrimination of changes in level and discrimination of changes in spectral shape for an eight tone complex sound a variety of different base spectral shapes were tested in some conditions level randomization was introduced to reduce the reliability of across interval changes in level increasing the amount of level variation degraded performance for the level discrimination task but had no effect on the shape discrimination task in all conditions sensitivity to changes in spectral shape was superior to sensitivity to changes in level consequently two models of central noise are evaluated in an attempt to explain these results one in which central noise acts prior to the formation of the likelihood ratio and one in which central noise degrades the likelihood ratio the former model is more successful in accounting for the data in a second experiment the detectability of a level increment to one component of a multitone complex was measured the frequency content of the complex was varied by systematically removing six components from a 23 component complex thresholds were measured for increments at three different signal frequencies a common trend in the data was that when there was a spectral gap directly above the signal frequency thresholds were lowest this result differs from the predictions of a simple channel model and contrasts with results presented by green and berg q j exp psychol 43a 449 458 1991

successive versus simultaneous comparison in auditory intensity discrimination the ability to discriminate between two brief sounds having identical frequency components but differing in the intensity of one or more of the components is studied the stimulus manipulations include randomizing the overall intensity of the sounds varying the number and spacing of the components and varying the interval of time between the sounds the results from the experiment in which interstimulus interval is manipulated clearly support a profile analysis mechanism that computes two rough spectral analyses stores a classification of these spectra in memory and compares the two stores this profile mechanism involves a simultaneous comparison of different components of the complex some remote from the signal frequency rather than a successive comparison of the difference in intensity at the signal frequency the simultaneous comparison process is more sensitive when the profile is composed of many components spaced over a wide frequency range

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

a dynamical system with hopf bifurcations and catastrophes a well known second order positive dynamical system describing the dynamics of a renewable resource together with its consumers prey predator model is first considered such a dynamical system is recognized to be a subtle hopf bifurcation without catastrophes then the model is slightly modified by including a control parameter which represents the indirect exploitation of the resource this new system is shown to have a much richer and interesting dynamics in particular catastrophes of the fold type hysteresis may arise moreover when the control value corresponding to the hopf bifurcation is greater than the lower threshold of the hysteresis one of the two transitions characterizing the catastrophe is a transition between a stableequilibrium and a limit cycle the results are illustrated in the control phase portrait

continuous point symmetries in group field theories we discuss the notion of symmetries in non local field theories characterized by integro differential equations of motion from a geometric perspective we then focus on group field theory gft models of quantum gravity and provide a general analysis of their continuous point symmetry transformations including the generalized conservation laws following from them

the interaction of steady state and hopf bifurcations in a two predator one prey competition model the existence of a stable periodic solution in the positive octant of a two predator one prey competition model is shown to result from the interaction of a steady state bifurcation with a hopf bifurcation this result confirms the conjectures based on numerical simulations of several authors that coexistence in the form of periodic oscillations in all three population sizes takes place for some parameter values of the model

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction