Nonlinear phenomena are commonly shown in the vocalization of animals and exerts different adaptive functions.Although some studies have pointed out that nonlinear phenomena can enhance the individual identification o...Nonlinear phenomena are commonly shown in the vocalization of animals and exerts different adaptive functions.Although some studies have pointed out that nonlinear phenomena can enhance the individual identification of male Odorrana tormota,whether the nonlinear phenomena play a specific role in the sexual selection of O.tormota remain unclear.Here we presented evidence that there was a significant negative correlation(Pearson:n=30,r=0.65,P<0.001)between the nonlinear phenomena content and snout-vent length in the male O.tormota,and two-choice amplexus experiments showed that female O.tormota preferred male with smaller body size containing higher nonlinear phenomena content in its calls.Phonotaxis experiments also revealed that females preferred calls with higher nonlinear phenomena content.Additionally,compared to the calls with lower nonlinear phenomena content and higher fundamental frequency,there was shorter response time in phonotactic behaviour of female induced by the calls with higher nonlinear phenomena content and lower fundamental frequency.We argue that the nonlinear phenomena content in the calls of male O.tormota can convey its body size information and may provide important clues for female frogs in darkened surroundings to identify males’body size during mate choice,meanwhile,higher nonlinear phenomena content in males’calls may increase the attractiveness of males to females.The results of this study provide confirmation that,for O.tormota,nonlinear phenomena have specific function in mate choice.展开更多
Fear and anxiety may be adaptive responses to life-threatening situations, and animals may communicate fear to others vocally. A fundamental understanding of fear inducing sounds is important for both wildlife conserv...Fear and anxiety may be adaptive responses to life-threatening situations, and animals may communicate fear to others vocally. A fundamental understanding of fear inducing sounds is important for both wildlife conservation and management because it helps us understand how to design repellents and also how （and why） animals may be negatively impacted by anthropogenic sounds. Nonlinear phenomena--sounds produced by the desynchronization of vibrations in a sound production system-are commonly found in stress-induced animal vocalizations, such as in alarm calls, mobbing calls, and fear screams. There are several functional hypotheses for these nonlinear phenomena. One specific hypothesis is the unpredictability hypothesis, which suggests that because nonlinear phenomena are more variable and somewhat unpredictable, animals are less likely to habituate to them. Animals should, therefore, have a prolonged response to sounds with nonlinear phenomena than sounds without them. Most of the studies involving nonlinear phenomena have used mammalian subjects and conspecific stimuli. Our study fo- cused on white-crowned sparrows （Zonotrichia leucophrys ssp. oriantha） and used synthesized acoustic stimuli to investigate behavioral responses to stimuli with and without nonlinear phenomena. We predicted that birds would be less relaxed after hearing a stimulus with a nonlinear component. We calculated the difference from baseline of proportion of time spent in relaxed behaviors and performed pair-wise comparisons between a pure tone control stimulus and each of three experimental stimuli, including a frequency jump up, a frequency jump down, and white noise. These comparisons showed that in the 30q50 s after the playback experiment, birds were significantly less relaxed after hearing noise or an abrupt frequency jump down an octave but not an abrupt frequency jump up an octave or a pure tone. Nonlinear phenomena, therefore, may be generally arousing to animals and may explain why these acoustic properties are commonly found in animal signals associated with fear [Current Zoology 60 （4）： 534-541, 2014].展开更多
We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. ...We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.展开更多
Male large odorous frogs(Odorrana graminea)have been shown to have a rich vocal repertoire and their calls contain harmonics that extend into the ultrasonic range,much like calls of male O.tormota,a sympatric species....Male large odorous frogs(Odorrana graminea)have been shown to have a rich vocal repertoire and their calls contain harmonics that extend into the ultrasonic range,much like calls of male O.tormota,a sympatric species.Whereas vocalizations of male O.tormota exhibit nonlinear characteristics and contain individual signatures,it is unclear whether or not those of O.graminea do.We carried out an extensive study of the vocalizations of male O.graminea with the goal of investigating whether they:(1)contained nonlinear phenomena(NLP),(2)carried individual signatures.We recorded and analyzed 1770 vocal calls from nine males.Their calls were classifiable into two distinct categories(one-note calls and multi-note calls).Of these,one-note complex/steep-frequency modulation call was the most abundant call-type.These calls showed diverse frequency modulation patterns,and abundant presence of NLP.Various basic spectral and temporal pa ra meters of such calls were individually distinct.Kruskal-Wallis Analysis of Rank test showed that the calls from individual males differed significantly.Subsequent discriminant function analysis(DFA)showed that 54.7%of the calls could be correctly assigned to individual.These results suggested that male O.graminea might be able to discriminate neighboring frogs from strangers acoustically.However,further research is necessary to demonstrate this capacity behaviorally.展开更多
Studying pup isolation calls of wild rodents provides background for developing new early-life animal models for biomedical research and drug testing.This study discovered a highly complex acoustic phenotype of pup is...Studying pup isolation calls of wild rodents provides background for developing new early-life animal models for biomedical research and drug testing.This study discovered a highly complex acoustic phenotype of pup isolation calls in 4–5-day-old Mongolian hamsters Allocricetulus curtatus.We analyzed the acoustic structure of 5,010 isolation calls emitted in the broad range of frequencies(sonic,below 20 kHz,and ultrasonic,from 20 to 128 kHz)by 23 pups during 2-min isolation test trials,1 trial per pup.In addition,we measured 5 body size parameters and the body weight of each pup.The calls could contain up to 3 independent fundamental frequencies in their spectra,the low(f0),the medium(g0),and the high(h0),or purely consisted of chaos in which the fundamental frequency could not be tracked.By presence/absence of the 3 fundamental frequencies or their combinations and chaos,we classifed calls into 6 distinctive categories(low-frequency[LF]-f0,LF-chaos,high-frequency[HF]-g0,HF-h0,HF-g0+h0,and HF-chaos)and estimated the relative abundance of calls in each category.Between categories,we compared acoustic parameters and estimated their relationship with pup body size index.We discuss the results of this study with data on the acoustics of pup isolation calls reported for other species of rodents.We conclude that such high complexity of Mongolian hamster pup isolation calls is unusual for rodents.Decreased acoustic complexity serves as a good indicator of autism spectrum disorders in knockout mouse models,which makes knockout hamster models prospective new wild animal model of neurodevelopmental disorders.展开更多
Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodyn...Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)equations.Cases with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are considered.In the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase.Moreover,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence.As a result,the profiles of safety factors also enter a nonlinear oscillation phase.In the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces.In the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.展开更多
Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these un...Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the wellknown drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.展开更多
The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stro...The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stroke currents.The effectiveness of numerical algorithms of nonlinear models and possibilities of their development for such transients are analyzed.Computer simulations carried out by application of EMTP show that nonlinear models of back-flashover and ZnO arresters work properly,while the implemented corona model can not be used for relatively large peak values of subsequent lightning return-stroke currents.展开更多
Nonlinear dynamic response represents the most important studies for structures subjected to a dynamic mo-tion so that it provides the researcher by an excellent information especially at critical design levels. The u...Nonlinear dynamic response represents the most important studies for structures subjected to a dynamic mo-tion so that it provides the researcher by an excellent information especially at critical design levels. The un-predictable nonlinearity in the structure appears when damage is inherited. Most times, the failure of the structure is related to the dynamic nonlinearity. With regard to the breathing phenomena for nonlinear struc-tural systems, very little is known about how the nonlinearities influence the response and the dynamic char-acteristics of cracked structures. In this research, dynamic nonlinearity is presented in damaged structure due to presence of a crack. The crack is assumed to be open and close simultaneously and then breathing. Effect of breathing phenomenon was studied deeply. Crack breathing is simulated at the crack surfaces using con-tact elements. The contact, geometrical, penalty, and spin stiffnesses are taken in consideration. In addition, effect of several important parameters such as rotor angular velocity and crack ratio are studied. The study showed that the breathing natural frequency of any structure is ranged between opened (no contact) and closed crack natural frequencies. The larger crack length, the more nonlinear disturbance in the dynamic re-sponse behavior. Also, at a critical crack length, some mode shapes tend to exchange and pass over with other modes. The presence of the mode interchanging and mode crossover was a guide on the nonlinear re-sponse for the cracked structure. The numerical modeling is achieved using ANSYS finite element program. Experimental data are used for validating the accurate use of contact elements in ANSYS environment.展开更多
Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evi...Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evidence of biphonation and other nonlinear phenomena.Here,we analyze the acoustic structure of captive wapiti vocalizations to compare the male bugle with 3 categories of distress vocalizations:neonate distress(capture)calls,calf isolation calls,and adult female isolation calls.These 4 high-arousal call categories serve a common general function in recruiting conspecifics but occur in different behavioral contexts(capture,isolation,reproduction).Our goal was to distinguish characteristics that vary in graded steps that may correspond to an animal’s age or size from characteristics that are unique to the bugle.Characteristics of the high and loud fundamental(G0)varied in an age/size-graded manner with a decrease in minimum G0,an increase in the maximum and range of G0,with no evidence of sex differences.The nonlinear phenomena of deterministic chaos,biphonation,and frequency jumps were present in all 4 call categories and became more common from the distress vocalizations of neonates to calves to adult females to the male bugle.Two temporal characteristics sharply distinguished the bugle from the 3 categories of distress vocalizations:these included a prolonged call duration and a maximum G0 that occurred much later in the call for the bugle than for distress vocalizations.Our results suggest that distress vocalizations of different age groups and the reproductive bugle of wapiti share a high G0,with age/size-graded changes in G0 and nonlinear phenomena,but differ sharply in temporal characteristics.展开更多
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
基金a grant from the Chinese Natural Science Foundation to Fang ZHANG(NSFC grants 3187223031640073)Anhui Provincial Key Laboratory of the Conservation and Exploitation of Biological Resources(No.591601)。
文摘Nonlinear phenomena are commonly shown in the vocalization of animals and exerts different adaptive functions.Although some studies have pointed out that nonlinear phenomena can enhance the individual identification of male Odorrana tormota,whether the nonlinear phenomena play a specific role in the sexual selection of O.tormota remain unclear.Here we presented evidence that there was a significant negative correlation(Pearson:n=30,r=0.65,P<0.001)between the nonlinear phenomena content and snout-vent length in the male O.tormota,and two-choice amplexus experiments showed that female O.tormota preferred male with smaller body size containing higher nonlinear phenomena content in its calls.Phonotaxis experiments also revealed that females preferred calls with higher nonlinear phenomena content.Additionally,compared to the calls with lower nonlinear phenomena content and higher fundamental frequency,there was shorter response time in phonotactic behaviour of female induced by the calls with higher nonlinear phenomena content and lower fundamental frequency.We argue that the nonlinear phenomena content in the calls of male O.tormota can convey its body size information and may provide important clues for female frogs in darkened surroundings to identify males’body size during mate choice,meanwhile,higher nonlinear phenomena content in males’calls may increase the attractiveness of males to females.The results of this study provide confirmation that,for O.tormota,nonlinear phenomena have specific function in mate choice.
文摘Fear and anxiety may be adaptive responses to life-threatening situations, and animals may communicate fear to others vocally. A fundamental understanding of fear inducing sounds is important for both wildlife conservation and management because it helps us understand how to design repellents and also how （and why） animals may be negatively impacted by anthropogenic sounds. Nonlinear phenomena--sounds produced by the desynchronization of vibrations in a sound production system-are commonly found in stress-induced animal vocalizations, such as in alarm calls, mobbing calls, and fear screams. There are several functional hypotheses for these nonlinear phenomena. One specific hypothesis is the unpredictability hypothesis, which suggests that because nonlinear phenomena are more variable and somewhat unpredictable, animals are less likely to habituate to them. Animals should, therefore, have a prolonged response to sounds with nonlinear phenomena than sounds without them. Most of the studies involving nonlinear phenomena have used mammalian subjects and conspecific stimuli. Our study fo- cused on white-crowned sparrows （Zonotrichia leucophrys ssp. oriantha） and used synthesized acoustic stimuli to investigate behavioral responses to stimuli with and without nonlinear phenomena. We predicted that birds would be less relaxed after hearing a stimulus with a nonlinear component. We calculated the difference from baseline of proportion of time spent in relaxed behaviors and performed pair-wise comparisons between a pure tone control stimulus and each of three experimental stimuli, including a frequency jump up, a frequency jump down, and white noise. These comparisons showed that in the 30q50 s after the playback experiment, birds were significantly less relaxed after hearing noise or an abrupt frequency jump down an octave but not an abrupt frequency jump up an octave or a pure tone. Nonlinear phenomena, therefore, may be generally arousing to animals and may explain why these acoustic properties are commonly found in animal signals associated with fear [Current Zoology 60 （4）： 534-541, 2014].
基金supported by the ITER-CN under Grant No. 2017YFE0301900carried out within the framework of the EUROfusion Consortium and received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under Grant Agreement No. 633053 (Project No. WP19-ER/ENEA-05)
文摘We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.
基金by a grant from the National Natural Science Foundation of China to F.Zhang(NSFC grants 31640073,31872230)。
文摘Male large odorous frogs(Odorrana graminea)have been shown to have a rich vocal repertoire and their calls contain harmonics that extend into the ultrasonic range,much like calls of male O.tormota,a sympatric species.Whereas vocalizations of male O.tormota exhibit nonlinear characteristics and contain individual signatures,it is unclear whether or not those of O.graminea do.We carried out an extensive study of the vocalizations of male O.graminea with the goal of investigating whether they:(1)contained nonlinear phenomena(NLP),(2)carried individual signatures.We recorded and analyzed 1770 vocal calls from nine males.Their calls were classifiable into two distinct categories(one-note calls and multi-note calls).Of these,one-note complex/steep-frequency modulation call was the most abundant call-type.These calls showed diverse frequency modulation patterns,and abundant presence of NLP.Various basic spectral and temporal pa ra meters of such calls were individually distinct.Kruskal-Wallis Analysis of Rank test showed that the calls from individual males differed significantly.Subsequent discriminant function analysis(DFA)showed that 54.7%of the calls could be correctly assigned to individual.These results suggested that male O.graminea might be able to discriminate neighboring frogs from strangers acoustically.However,further research is necessary to demonstrate this capacity behaviorally.
文摘Studying pup isolation calls of wild rodents provides background for developing new early-life animal models for biomedical research and drug testing.This study discovered a highly complex acoustic phenotype of pup isolation calls in 4–5-day-old Mongolian hamsters Allocricetulus curtatus.We analyzed the acoustic structure of 5,010 isolation calls emitted in the broad range of frequencies(sonic,below 20 kHz,and ultrasonic,from 20 to 128 kHz)by 23 pups during 2-min isolation test trials,1 trial per pup.In addition,we measured 5 body size parameters and the body weight of each pup.The calls could contain up to 3 independent fundamental frequencies in their spectra,the low(f0),the medium(g0),and the high(h0),or purely consisted of chaos in which the fundamental frequency could not be tracked.By presence/absence of the 3 fundamental frequencies or their combinations and chaos,we classifed calls into 6 distinctive categories(low-frequency[LF]-f0,LF-chaos,high-frequency[HF]-g0,HF-h0,HF-g0+h0,and HF-chaos)and estimated the relative abundance of calls in each category.Between categories,we compared acoustic parameters and estimated their relationship with pup body size index.We discuss the results of this study with data on the acoustics of pup isolation calls reported for other species of rodents.We conclude that such high complexity of Mongolian hamster pup isolation calls is unusual for rodents.Decreased acoustic complexity serves as a good indicator of autism spectrum disorders in knockout mouse models,which makes knockout hamster models prospective new wild animal model of neurodevelopmental disorders.
基金Project supported by the National Key R&D Program of China(Grant No.2022YFE03090000)the National Natural Science Foundation of China(Grant No.11925501)the Fundament Research Funds for the Central Universities(Grant No.DUT22ZD215)。
文摘Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)equations.Cases with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are considered.In the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase.Moreover,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence.As a result,the profiles of safety factors also enter a nonlinear oscillation phase.In the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces.In the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.
基金supported by National Natural Science Fundation of China (Nos. 11235009 and 11905097)Fundamental Research Fund for Chinese Central Universities (No. 2019FZA3003)carried out within the framework of the EUROfusion Consortium and received funding from Euratom research and training programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053 (Project No. WP19-ER/ENEA-05)。
文摘Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the wellknown drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.
文摘The paper presents some problems of lightning overvoltage modeling in transmission lines with nonlinear elements.The presented results were obtained mostly for fast front transients of subsequent lightning return stroke currents.The effectiveness of numerical algorithms of nonlinear models and possibilities of their development for such transients are analyzed.Computer simulations carried out by application of EMTP show that nonlinear models of back-flashover and ZnO arresters work properly,while the implemented corona model can not be used for relatively large peak values of subsequent lightning return-stroke currents.
文摘Nonlinear dynamic response represents the most important studies for structures subjected to a dynamic mo-tion so that it provides the researcher by an excellent information especially at critical design levels. The un-predictable nonlinearity in the structure appears when damage is inherited. Most times, the failure of the structure is related to the dynamic nonlinearity. With regard to the breathing phenomena for nonlinear struc-tural systems, very little is known about how the nonlinearities influence the response and the dynamic char-acteristics of cracked structures. In this research, dynamic nonlinearity is presented in damaged structure due to presence of a crack. The crack is assumed to be open and close simultaneously and then breathing. Effect of breathing phenomenon was studied deeply. Crack breathing is simulated at the crack surfaces using con-tact elements. The contact, geometrical, penalty, and spin stiffnesses are taken in consideration. In addition, effect of several important parameters such as rotor angular velocity and crack ratio are studied. The study showed that the breathing natural frequency of any structure is ranged between opened (no contact) and closed crack natural frequencies. The larger crack length, the more nonlinear disturbance in the dynamic re-sponse behavior. Also, at a critical crack length, some mode shapes tend to exchange and pass over with other modes. The presence of the mode interchanging and mode crossover was a guide on the nonlinear re-sponse for the cracked structure. The numerical modeling is achieved using ANSYS finite element program. Experimental data are used for validating the accurate use of contact elements in ANSYS environment.
基金The University of Winnipeg and The University of Winnipeg Foundation contributed funding to this research.
文摘Variation in the vocal behavior of nonhuman vertebrates includes graded transitions and more dramatic changes.Wapiti males produce a reproductive bugle that has a fundamental frequency that surpasses 2,000 Hz with evidence of biphonation and other nonlinear phenomena.Here,we analyze the acoustic structure of captive wapiti vocalizations to compare the male bugle with 3 categories of distress vocalizations:neonate distress(capture)calls,calf isolation calls,and adult female isolation calls.These 4 high-arousal call categories serve a common general function in recruiting conspecifics but occur in different behavioral contexts(capture,isolation,reproduction).Our goal was to distinguish characteristics that vary in graded steps that may correspond to an animal’s age or size from characteristics that are unique to the bugle.Characteristics of the high and loud fundamental(G0)varied in an age/size-graded manner with a decrease in minimum G0,an increase in the maximum and range of G0,with no evidence of sex differences.The nonlinear phenomena of deterministic chaos,biphonation,and frequency jumps were present in all 4 call categories and became more common from the distress vocalizations of neonates to calves to adult females to the male bugle.Two temporal characteristics sharply distinguished the bugle from the 3 categories of distress vocalizations:these included a prolonged call duration and a maximum G0 that occurred much later in the call for the bugle than for distress vocalizations.Our results suggest that distress vocalizations of different age groups and the reproductive bugle of wapiti share a high G0,with age/size-graded changes in G0 and nonlinear phenomena,but differ sharply in temporal characteristics.
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
