Modeling synchronized calling behavior of Japanese tree frogs

Solvable model of driven matter with pinning

We present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls.

Diverse behaviors in non-uniform chiral and non-chiral swarmalators

We study the emergent behaviors of a population of swarming coupled oscillators, dubbed swarmalators. Previous work considered the simplest, idealized case: identical swarmalators with global coupling. Here we expand this work by adding more realistic features: local coupling, non-identical natural frequencies, and chirality. This more realistic model generates a variety of new behaviors including lattices of vortices, beating clusters, and interacting phase waves. Similar behaviors are found across natural and artificial micro-scale collective systems, including social slime mold, spermatozoa vortex arrays, and Quincke rollers. Our results indicate a wide range of future use cases, both to aid characterization and understanding of natural swarms, and to design complex interactions in collective systems from soft and active matter to micro-robotics.

Collective behavior of swarmalators on a ring

We study the collective behavior of swarmalators, generalizations of phase oscillators that both sync and swarm, confined to move on a one-dimensional (1D) ring. This simple model captures the essence of movement in two or three dimensions, but has the benefit of being solvable: most of the collective states and their bifurcations can be specified exactly. The model also captures the behavior of real-world swarmalators which swarm in quasi-1D rings such as bordertaxic vinegar eels and sperm.

Visualization of a chorus structure in multiple frog species by a sound discrimination device

We developed a sound discrimination device to identify and localize the species of nocturnal animals in their natural habitat. The sound discrimination device is equipped with a microphone, a light-emitting diode, and a band-pass filter. By tuning the center frequency of the filter to include a dominant frequency of the calls of a focal species, we enable the device to be illuminated only when detecting the calls of the focal species. In experiments in a laboratory room, we tuned the sound discrimination devices to detect the calls of Hyla japonica or Rhacophorus schlegelii and broadcast the frog calls from loudspeakers. By analyzing the illumination pattern of the devices, we successfully identified and localized the two kinds of sound sources. Next, we placed the sound discrimination devices in a field site where actual male frogs (H. japonica and R. schlegelii) produced sounds. The analysis of the illumination pattern demonstrates the efficacy of the developed devices in a natural environment and also enables us to extract pairs of male frogs that significantly overlapped or alternated their calls.

Interaction mechanisms quantified from dynamical features of frog choruses

We employ a mathematical model (a phase oscillator model) to describe the deterministic and stochastic features of frog choruses in which male frogs attempt to avoid call overlaps. The mathematical model with a general interaction term is identified using a Bayesian approach, and it qualitatively reproduces the stationary and dynamical features of the empirical data. In addition, we quantify the magnitude of attention paid among the male frogs from the identified model, and then analyse the relationship between attention and behavioural parameters using a statistical approach. Our analysis demonstrates a negative correlation between attention and inter-frog distance, and also suggests a behavioural strategy in which male frogs selectively attend to a less attractive male frog (i.e. a male producing calls at longer intervals) in order to more effectively advertise their superior relative attractiveness to females.

Frequency and Phase Characteristics of Candle Flame Oscillation

The combustion of candles exhibits a variety of dynamical behaviors. Binding several candles together will result in flickering of candle flames, which is generally described as a nonlinear oscillator. The impact on the frequency of the flame by several factors, such as the arrangement, the number and the asymmetry of the oscillators, is discussed. Experimental results show that the frequency gradually decreases as the number of candles increases in the case of an isolated oscillator, while alternation between the in-phase and the anti-phase synchronization appears in a coupled system of two oscillators. Moreover, envelopes in the amplitude of the oscillatory luminance are displayed when candles are coupled asymmetrically. Since the coupling between oscillators is dominated by thermal radiation, a “overlapped peaks model” is proposed to phenomenologically explain the relationship between temperature distribution, coupling strength and the collective behavior in coupled system of candle oscillators in both symmetric and asymmetric cases.

Mathematical modelling and application of frog choruses as an autonomous distributed communication system

Interactions using various sensory cues produce sophisticated behaviour in animal swarms, e.g. the foraging behaviour of ants and the flocking of birds and fish. Here, we investigate the behavioural mechanisms of frog choruses from the viewpoints of mathematical modelling and its application. Empirical data on male Japanese tree frogs demonstrate that (1) neighbouring male frogs avoid call overlaps with each other over a short time scale and (2) they collectively switch between the calling state and the silent state over a long time scale. To reproduce these features, we propose a mathematical model in which separate dynamical models spontaneously switch due to a stochastic process depending on the internal dynamics of respective frogs and also the interactions among the frogs. Next, the mathematical model is applied to the control of a wireless sensor network in which multiple sensor nodes send a data packet towards their neighbours so as to deliver the packet to a gateway node by multi-hop communication. Numerical simulation demonstrates that (1) neighbouring nodes can avoid a packet collision over a short time scale by alternating the timing of data transmission and (2) all the nodes collectively switch their states over a long time scale, establishing high network connectivity while reducing network power consumption. Consequently, this study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology that is applicable to the control of a wireless sensor network.

Ring states in swarmalator systems

Synchronization is a universal phenomenon, occurring in systems as disparate as Japanese tree frogs and Josephson junctions. Typically, the elements of synchronizing systems adjust the phases of their oscillations, but not their positions in space. The reverse scenario is found in swarming systems, such as schools of fish or flocks of birds; now the elements adjust their positions in space, but without (noticeably) changing their internal states. Systems capable of both swarming and synchronizing, dubbed swarmalators, have recently been proposed, and analyzed in the continuum limit. Here, we extend this work by studying finite populations of swarmalators, whose phase similarity affects both their spatial attraction and repulsion. We find ring states, and compute criteria for their existence and stability. Larger populations can form annular distributions, whose density we calculate explicitly. These states may be observable in groups of Japanese tree frogs, ferromagnetic colloids, and other systems with an interplay between swarming and synchronization.

Asymmetry in cilia configuration induces hydrodynamic phase locking

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

Size Effect on Call Properties of Japanese Tree Frogs Revealed by Audio-Processing Technique

[abstFig src='/00290001/23.jpg' width='300' text='Calling behavior of a male Japanese Tree Frog' ] Sensing the external environment is a core function of robots and autonomous mechanics. This function is useful for monitoring and analyzing the ecosystem for our deeper understanding of the nature and accomplishing the sustainable ecosystem. Here, we investigate calling behavior of male frogs by applying audio-processing technique on multiple audio data. In general, male frogs call from their breeding site, and a female frog approaches one of the males by hearing their calls. First, we conducted an indoor experiment to record spontaneous calling behavior of three male Japanese tree frogs, and then separated their call signals according to independent component analysis. The analysis of separated signals shows that chorus size (i.e., the number of calling frogs) has a positive effect on call number, inter-call intervals, and chorus duration. We speculate that a competition in a large chorus encourages the male frogs to make their call properties more attractive to conspecific females.

Experimental and modeling analysis of asymmetrical on-off oscillation in coupled non-identical inverted bottle oscillators

Upside-down bottles containing water which are common in our daily life exhibit rich vibration dynamics. Rich dynamic regimes are observed in bottle oscillators by directly measuring the pressure difference between inside and outside of a bottle with the aid of pressure sensors. We observe experimentally that an asymmetrical oscillation process between the outflow of water and the inflow of air is formed in a single bottle oscillator and, in addition, a kind of 2:1 frequency synchronization occurs in a coupled system of two non-identical bottle oscillators. The peak values of the oscillation of pressure differences between inside and outside of the bottle decease as the height of the liquid surface steps down, while the oscillation period increases gradually. The theoretical model of the oscillator is amended to understand the regimes in the experiment by introducing time-dependent parameters related to the asymmetrical oscillation processes. Our numerical results based on the model fit well with the experimental ones.

Call intercalation in dyadic interactions in natural choruses of Johnstone's whistling frog Eleutherodactylus johnstonei (Anura: Eleutherodactylidae)

Communal signaling increases the likelihood of acoustic interference and impairs mate choice; consequently, mechanisms of interference avoidance are expected. Adjustment of the timing of the calls between signalers, specifically call alternation, is probably the most efficient strategy. For this reason, in the present study we analyzed call timing in dyads of males of E. johnstonei in six natural assemblages. We addressed whether males entrain their calls with those of other males at the assemblage and if they show selective attention in relation to perceived amplitude of the other males' calls, inter-male distance, or intrinsic call features (call duration, period or dominant frequency). We expected males to selectively attend to closer or louder males and/or to those of higher or similar attractiveness for females than themselves, because those would be their strongest competitors. We found that most males intercalated their calls with those of at least one male. In assemblages of 3 individuals, males seemed to attend to a fixed number of males regardless of their characteristics. In assemblages of more than 3 individuals, the perceived amplitude of the call of the neighboring male was higher, and the call periods of the males were more similar in alternating dyads than in the non-alternating ones. At the proximate level, selective attention based on perceived amplitude may relate to behavioral hearing thresholds. Selective attention based on the similarity of call periods may relate to the properties of the call oscillators controlling calling rhythms. At the ultimate level, selective attention may be related to the likelihood of acoustic competition for females.

Experimental and theoretical approach for the clustering of globally coupled density oscillators based on phase response

We investigated the phase-response curve of a coupled system of density oscillators with an analytical approach. The behaviors of two-, three-, and four-coupled systems seen in the experiments were reproduced by the model considering the phase-response curve. Especially in a four-coupled system, the clustering state and its incidence rate as functions of the coupling strength are well reproduced with this approach. Moreover, we confirmed that the shape of the phase-response curve we obtained analytically was close to that observed in the experiment where a perturbation is added to a single-density oscillator. We expect that this approach to obtaining the phase-response curve is general in the sense that it could be applied to coupled systems of other oscillators such as electrical-circuit oscillators, metronomes, and so on.

Spatio-temporal dynamics in collective frog choruses examined by mathematical modeling and field observations

This paper reports theoretical and experimental studies on spatio-temporal dynamics in the choruses of male Japanese tree frogs. First, we theoretically model their calling times and positions as a system of coupled mobile oscillators. Numerical simulation of the model as well as calculation of the order parameters show that the spatio-temporal dynamics exhibits bistability between two-cluster antisynchronization and wavy antisynchronization, by assuming that the frogs are attracted to the edge of a simple circular breeding site. Second, we change the shape of the breeding site from the circle to rectangles including a straight line, and evaluate the stability of two-cluster and wavy antisynchronization. Numerical simulation shows that two-cluster antisynchronization is more frequently observed than wavy antisynchronization. Finally, we recorded frog choruses at an actual paddy field using our sound-imaging method. Analysis of the video demonstrated a consistent result with the aforementioned simulation: namely, two-cluster antisynchronization was more frequently realized.

Plastic bottle oscillator as an on-off-type oscillator: experiments, modeling, and stability analyses of single and coupled systems

An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations.

Hysteresis in the gait transition of a quadruped investigated using simple body mechanical and oscillator network models

We investigated the dynamics of quadrupedal locomotion by constructing a simple quadruped model that consists of a body mechanical model and an oscillator network model. The quadruped model has front and rear bodies connected by a waist joint with a torsional spring and damper system and four limbs controlled by command signals from the oscillator network model. The simulation results reveal that the quadruped model produces various gait patterns through dynamic interactions among the body mechanical system, the oscillator network system, and the environment. They also show that it undergoes a gait transition induced by changes in the waist joint stiffness and the walking speed. In addition, the gait pattern transition exhibits a hysteresis similar to that observed in human and animal locomotion. We examined the hysteresis mechanism from a dynamic viewpoint.

Sound imaging of nocturnal animal calls in their natural habitat

We present a novel method for imaging acoustic communication between nocturnal animals. Investigating the spatio-temporal calling behavior of nocturnal animals, e.g., frogs and crickets, has been difficult because of the need to distinguish many animals' calls in noisy environments without being able to see them. Our method visualizes the spatial and temporal dynamics using dozens of sound-to-light conversion devices (called "Firefly") and an off-the-shelf video camera. The Firefly, which consists of a microphone and a light emitting diode, emits light when it captures nearby sound. Deploying dozens of Fireflies in a target area, we record calls of multiple individuals through the video camera. We conduct two experiments, one indoors and the other in the field, using Japanese tree frogs (Hyla japonica). The indoor experiment demonstrates that our method correctly visualizes Japanese tree frogs' calling behavior. It has confirmed the known behavior; two frogs call synchronously or in anti-phase synchronization. The field experiment (in a rice paddy where Japanese tree frogs live) also visualizes the same calling behavior to confirm anti-phase synchronization in the field. Experimental results confirm that our method can visualize the calling behavior of nocturnal animals in their natural habitat.

Complex and transitive synchronization in a frustrated system of calling frogs

This letter reports synchronization phenomena and mathematical modeling on a frustrated system of living beings, or Japanese tree frogs (Hyla japonica). While an isolated male Japanese tree frog calls nearly periodically, he can hear sounds including calls of other males. Therefore, the spontaneous calling behavior of interacting males can be understood as a system of coupled oscillators. We construct a simple but biologically reasonable model based on the experimental results of two frogs, extend the model to a system of three frogs, and theoretically predict the occurrence of rich synchronization phenomena, such as triphase synchronization and 1:2 antiphase synchronization. In addition, we experimentally verify the theoretical prediction by ethological experiments on the calling behavior of three frogs and time series analysis on recorded sound data. Note that the calling behavior of three male Japanese tree frogs is frustrated because almost perfect antiphase synchronization is robustly observed in a system of two male frogs. Thus, nonlinear dynamics of the three-frogs system should be far from trivial.

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator driven by weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.