An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter $alpha$ on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability. Linear stability analysis reveals the stable regions of coherent states with different winding numbers $q$. Within certain $alpha$ ranges, the system settles into stable traveling wave solutions despite the coherent states also being linearly stable. For around $alpha approx 0.46pi$, the system displays the most frequent metastable transitions between coherent states and partially synchronized states, while for $alpha$ closer to $pi/2$, metastable transitions arise between partially synchronized states and modulated states. This model captures metastable dynamics akin to brain activity, offering insights into the synchronization of brain networks.
{"title":"Metastability of multi-population Kuramoto-Sakaguchi oscillators","authors":"Bojun Li, Nariya Uchida","doi":"arxiv-2405.15396","DOIUrl":"https://doi.org/arxiv-2405.15396","url":null,"abstract":"An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is\u0000investigated, focusing on the influence of the phase-lag parameter $alpha$ on\u0000the collective dynamics. For oscillator populations coupled on a ring, we\u0000obtained a wide variety of spatiotemporal patterns, including coherent states,\u0000traveling waves, partially synchronized states, modulated states, and\u0000incoherent states. Back-and-forth transitions between these states are found,\u0000which suggest metastability. Linear stability analysis reveals the stable\u0000regions of coherent states with different winding numbers $q$. Within certain\u0000$alpha$ ranges, the system settles into stable traveling wave solutions\u0000despite the coherent states also being linearly stable. For around $alpha\u0000approx 0.46pi$, the system displays the most frequent metastable transitions\u0000between coherent states and partially synchronized states, while for $alpha$\u0000closer to $pi/2$, metastable transitions arise between partially synchronized\u0000states and modulated states. This model captures metastable dynamics akin to\u0000brain activity, offering insights into the synchronization of brain networks.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A wide variety of engineered and natural systems are modelled as networks of coupled nonlinear oscillators. In nature, the intrinsic frequencies of these oscillators are not constant in time. Here, we probe the effect of such a temporal heterogeneity on coupled oscillator networks, through the lens of the Kuramoto model. To do this, we shuffle repeatedly the intrinsic frequencies among the oscillators at either random or regular time intervals. What emerges is the remarkable effect that frequent shuffling induces earlier onset (i.e., at a lower coupling) of synchrony among the oscillator phases. Our study provides a novel strategy to induce and control synchrony under resource constraints. We demonstrate our results analytically and in experiments with a network of Wien Bridge oscillators with internal frequencies being shuffled in time.
{"title":"Synchronization through frequency shuffling","authors":"Manaoj Aravind, Vaibhav Pachaulee, Mrinal Sarkar, Ishant Tiwari, Shamik Gupta, P. Parmananda","doi":"arxiv-2405.13569","DOIUrl":"https://doi.org/arxiv-2405.13569","url":null,"abstract":"A wide variety of engineered and natural systems are modelled as networks of\u0000coupled nonlinear oscillators. In nature, the intrinsic frequencies of these\u0000oscillators are not constant in time. Here, we probe the effect of such a\u0000temporal heterogeneity on coupled oscillator networks, through the lens of the\u0000Kuramoto model. To do this, we shuffle repeatedly the intrinsic frequencies\u0000among the oscillators at either random or regular time intervals. What emerges\u0000is the remarkable effect that frequent shuffling induces earlier onset (i.e.,\u0000at a lower coupling) of synchrony among the oscillator phases. Our study\u0000provides a novel strategy to induce and control synchrony under resource\u0000constraints. We demonstrate our results analytically and in experiments with a\u0000network of Wien Bridge oscillators with internal frequencies being shuffled in\u0000time.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a geometric investigation of curious dynamical behaviors previously reported in Kuramoto models with two sub-populations. Our study demonstrates that chimeras and traveling waves in such models are associated with the birth of geometric phase. Although manifestations of geometric phase are frequent in various fields of Physics, this is the first time (to our best knowledge) that such a phenomenon is exposed in ensembles of Kuramoto oscillators or, more broadly, in complex systems.
{"title":"Phase holonomy underlies puzzling temporal patterns in Kuramoto models with two sub-populations","authors":"Aladin Crnkić, Vladimir Jaćimović","doi":"arxiv-2405.09696","DOIUrl":"https://doi.org/arxiv-2405.09696","url":null,"abstract":"We present a geometric investigation of curious dynamical behaviors\u0000previously reported in Kuramoto models with two sub-populations. Our study\u0000demonstrates that chimeras and traveling waves in such models are associated\u0000with the birth of geometric phase. Although manifestations of geometric phase\u0000are frequent in various fields of Physics, this is the first time (to our best\u0000knowledge) that such a phenomenon is exposed in ensembles of Kuramoto\u0000oscillators or, more broadly, in complex systems.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cong Wang, Zhongqiu Wang, Jianhua Yang, Miguel A. F. Sanjuán, Gong Tao, Zhen Shan, Mengen Shen
Ultra-high frequency linear frequency modulation (UHF-LFM) signal, as a kind of typical non-stationary signal, has been widely used in microwave radar and other fields, with advantages such as long transmission distance, strong anti-interference ability, and wide bandwidth. Utilizing optimal dynamics response has unique advantages in weak feature identification under strong background noise. We propose a new stochastic resonance method in an asymmetric bistable system with the time-varying parameter to handle this special non-stationary signal. Interestingly, the nonlinear response exhibits multiple stochastic resonances (MSR) and inverse stochastic resonances (ISR) under UHF-LFM signal excitation, and some resonance regions may deviate or collapse due to the influence of system asymmetry. In addition, we analyze the responses of each resonance region and the mechanism and evolution law of each resonance region in detail. Finally, we significantly expand the resonance region within the parameter range by optimizing the time scale, which verifies the effectiveness of the proposed time-varying scale method. The mechanism and evolution law of MSR and ISR will provide references for researchers in related fields.
{"title":"Multiple stochastic resonances and inverse stochastic resonances in asymmetric bistable system under the ultra-high frequency excitation","authors":"Cong Wang, Zhongqiu Wang, Jianhua Yang, Miguel A. F. Sanjuán, Gong Tao, Zhen Shan, Mengen Shen","doi":"arxiv-2405.07804","DOIUrl":"https://doi.org/arxiv-2405.07804","url":null,"abstract":"Ultra-high frequency linear frequency modulation (UHF-LFM) signal, as a kind\u0000of typical non-stationary signal, has been widely used in microwave radar and\u0000other fields, with advantages such as long transmission distance, strong\u0000anti-interference ability, and wide bandwidth. Utilizing optimal dynamics\u0000response has unique advantages in weak feature identification under strong\u0000background noise. We propose a new stochastic resonance method in an asymmetric\u0000bistable system with the time-varying parameter to handle this special\u0000non-stationary signal. Interestingly, the nonlinear response exhibits multiple\u0000stochastic resonances (MSR) and inverse stochastic resonances (ISR) under\u0000UHF-LFM signal excitation, and some resonance regions may deviate or collapse\u0000due to the influence of system asymmetry. In addition, we analyze the responses\u0000of each resonance region and the mechanism and evolution law of each resonance\u0000region in detail. Finally, we significantly expand the resonance region within\u0000the parameter range by optimizing the time scale, which verifies the\u0000effectiveness of the proposed time-varying scale method. The mechanism and\u0000evolution law of MSR and ISR will provide references for researchers in related\u0000fields.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"160 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solids are rigid, which means that when left undisturbed, their structures are nearly static. It follows that these structures depend on history -- but it is surprising that they hold readable memories of past events. Here we review the research that has recently flourished around mechanical memory formation, beginning with amorphous solids' various memories of deformation and mesoscopic models based on particle rearrangements. We describe how these concepts apply to a much wider range of solids and glassy matter -- and how they are a bridge to memory and physical computing in mechanical metamaterials. An understanding of memory in all these solids can potentially be the basis for designing or training functionality into materials. Just as important is memory's value for understanding matter whenever it is complex, frustrated, and out of equilibrium.
{"title":"Mechanical memories in solids, from disorder to design","authors":"Joseph D. Paulsen, Nathan C. Keim","doi":"arxiv-2405.08158","DOIUrl":"https://doi.org/arxiv-2405.08158","url":null,"abstract":"Solids are rigid, which means that when left undisturbed, their structures\u0000are nearly static. It follows that these structures depend on history -- but it\u0000is surprising that they hold readable memories of past events. Here we review\u0000the research that has recently flourished around mechanical memory formation,\u0000beginning with amorphous solids' various memories of deformation and mesoscopic\u0000models based on particle rearrangements. We describe how these concepts apply\u0000to a much wider range of solids and glassy matter -- and how they are a bridge\u0000to memory and physical computing in mechanical metamaterials. An understanding\u0000of memory in all these solids can potentially be the basis for designing or\u0000training functionality into materials. Just as important is memory's value for\u0000understanding matter whenever it is complex, frustrated, and out of\u0000equilibrium.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guillaume Pourcel, Mirko Goldmann, Ingo Fischer, Miguel C. Soriano
Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning setting, the network's parameters are adapted during a training phase to match the requirements of a given task/problem increasing its computational capabilities. After the training, the network parameters are kept fixed to exploit the learned computations. The static parameters thereby render the network unadaptive to changing conditions, such as external or internal perturbation. In this manuscript, we demonstrate how keeping parts of the network adaptive even after the training enhances its functionality and robustness. Here, we utilize the conceptor framework and conceptualize an adaptive control loop analyzing the network's behavior continuously and adjusting its time-varying internal representation to follow a desired target. We demonstrate how the added adaptivity of the network supports the computational functionality in three distinct tasks: interpolation of temporal patterns, stabilization against partial network degradation, and robustness against input distortion. Our results highlight the potential of adaptive networks in machine learning beyond training, enabling them to not only learn complex patterns but also dynamically adjust to changing environments, ultimately broadening their applicability.
{"title":"Adaptive control of recurrent neural networks using conceptors","authors":"Guillaume Pourcel, Mirko Goldmann, Ingo Fischer, Miguel C. Soriano","doi":"arxiv-2405.07236","DOIUrl":"https://doi.org/arxiv-2405.07236","url":null,"abstract":"Recurrent Neural Networks excel at predicting and generating complex\u0000high-dimensional temporal patterns. Due to their inherent nonlinear dynamics\u0000and memory, they can learn unbounded temporal dependencies from data. In a\u0000Machine Learning setting, the network's parameters are adapted during a\u0000training phase to match the requirements of a given task/problem increasing its\u0000computational capabilities. After the training, the network parameters are kept\u0000fixed to exploit the learned computations. The static parameters thereby render\u0000the network unadaptive to changing conditions, such as external or internal\u0000perturbation. In this manuscript, we demonstrate how keeping parts of the\u0000network adaptive even after the training enhances its functionality and\u0000robustness. Here, we utilize the conceptor framework and conceptualize an\u0000adaptive control loop analyzing the network's behavior continuously and\u0000adjusting its time-varying internal representation to follow a desired target.\u0000We demonstrate how the added adaptivity of the network supports the\u0000computational functionality in three distinct tasks: interpolation of temporal\u0000patterns, stabilization against partial network degradation, and robustness\u0000against input distortion. Our results highlight the potential of adaptive\u0000networks in machine learning beyond training, enabling them to not only learn\u0000complex patterns but also dynamically adjust to changing environments,\u0000ultimately broadening their applicability.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we consider the influence of a periodic sequence of Gaussian pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We found that on the way to complete spatial synchronization one can observe a number of variations of chimera states that are not typical for the parameter range under consideration. For example, the following modes were found: breathing chimera, chimera with intermittency in the incoherent part, traveling chimera with strong intermittency, and others. For comparison, here we also consider the impact of a harmonic influence on the same chimera, and to preserve the generality of the conclusions, we compare the regimes caused by both a purely positive harmonic influence and a positive-negative one.
{"title":"Impact of pulse exposure on chimera state in ensemble of FitzHugh-Nagumo systems","authors":"Elena Rybalova, Nadezhda Semenova","doi":"arxiv-2405.06833","DOIUrl":"https://doi.org/arxiv-2405.06833","url":null,"abstract":"In this article we consider the influence of a periodic sequence of Gaussian\u0000pulses on a chimera state in a ring of coupled FitzHugh-Nagumo systems. We\u0000found that on the way to complete spatial synchronization one can observe a\u0000number of variations of chimera states that are not typical for the parameter\u0000range under consideration. For example, the following modes were found:\u0000breathing chimera, chimera with intermittency in the incoherent part, traveling\u0000chimera with strong intermittency, and others. For comparison, here we also\u0000consider the impact of a harmonic influence on the same chimera, and to\u0000preserve the generality of the conclusions, we compare the regimes caused by\u0000both a purely positive harmonic influence and a positive-negative one.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Deep neural networks give us a powerful method to model the training dataset's relationship between input and output. We can regard that as a complex adaptive system consisting of many artificial neurons that work as an adaptive memory as a whole. The network's behavior is training dynamics with a feedback loop from the evaluation of the loss function. We already know the training response can be constant or shows power law-like aging in some ideal situations. However, we still have gaps between those findings and other complex phenomena, like network fragility. To fill the gap, we introduce a very simple network and analyze it. We show the training response consists of some different factors based on training stages, activation functions, or training methods. In addition, we show feature space reduction as an effect of stochastic training dynamics, which can result in network fragility. Finally, we discuss some complex phenomena of deep networks.
{"title":"A simple theory for training response of deep neural networks","authors":"Kenichi Nakazato","doi":"arxiv-2405.04074","DOIUrl":"https://doi.org/arxiv-2405.04074","url":null,"abstract":"Deep neural networks give us a powerful method to model the training\u0000dataset's relationship between input and output. We can regard that as a\u0000complex adaptive system consisting of many artificial neurons that work as an\u0000adaptive memory as a whole. The network's behavior is training dynamics with a\u0000feedback loop from the evaluation of the loss function. We already know the\u0000training response can be constant or shows power law-like aging in some ideal\u0000situations. However, we still have gaps between those findings and other\u0000complex phenomena, like network fragility. To fill the gap, we introduce a very\u0000simple network and analyze it. We show the training response consists of some\u0000different factors based on training stages, activation functions, or training\u0000methods. In addition, we show feature space reduction as an effect of\u0000stochastic training dynamics, which can result in network fragility. Finally,\u0000we discuss some complex phenomena of deep networks.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"233 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Moritz Thümler, Shesha G. M. Srinivas, Malte Schröder, Marc Timme
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of textit{complex locked states} for coupling strengths $K$ below the transition $K^{(text{pl})}$ to classical textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'
{"title":"Synchrony for weak coupling in the complexified Kuramoto model","authors":"Moritz Thümler, Shesha G. M. Srinivas, Malte Schröder, Marc Timme","doi":"arxiv-2404.19637","DOIUrl":"https://doi.org/arxiv-2404.19637","url":null,"abstract":"We present the finite-size Kuramoto model analytically continued from real to\u0000complex variables and analyze its collective dynamics. For strong coupling,\u0000synchrony appears through locked states that constitute attractors, as for the\u0000real-variable system. However, synchrony persists in the form of\u0000textit{complex locked states} for coupling strengths $K$ below the transition\u0000$K^{(text{pl})}$ to classical textit{phase locking}. Stable complex locked\u0000states indicate a locked sub-population of zero mean frequency in the\u0000real-variable model and their imaginary parts help identifying which units\u0000comprise that sub-population. We uncover a second transition at\u0000$K'<K^{(text{pl})}$ below which complex locked states become linearly unstable\u0000yet still exist for arbitrarily small coupling strengths.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a model of the central pattern generator (CPG) network that can control gait transitions in hexapod robots in a simple manner based on phase reduction. The CPG network consists of six weakly coupled limit-cycle oscillators, whose synchronization dynamics can be described by six phase equations through phase reduction. Focusing on the transitions between the hexapod gaits with specific symmetries, the six phase equations of the CPG network can further be reduced to two independent equations for the phase differences. By choosing appropriate coupling functions for the network, we can achieve desired synchronization dynamics regardless of the detailed properties of the limit-cycle oscillators used for the CPG. The effectiveness of our CPG network is demonstrated by numerical simulations of gait transitions between the wave, tetrapod, and tripod gaits, using the FitzHugh-Nagumo oscillator as the CPG unit.
{"title":"A Central Pattern Generator Network for Simple Control of Gait Transitions in Hexapod Robots based on Phase Reduction","authors":"Norihisa Namura, Hiroya Nakao","doi":"arxiv-2404.17139","DOIUrl":"https://doi.org/arxiv-2404.17139","url":null,"abstract":"We present a model of the central pattern generator (CPG) network that can\u0000control gait transitions in hexapod robots in a simple manner based on phase\u0000reduction. The CPG network consists of six weakly coupled limit-cycle\u0000oscillators, whose synchronization dynamics can be described by six phase\u0000equations through phase reduction. Focusing on the transitions between the\u0000hexapod gaits with specific symmetries, the six phase equations of the CPG\u0000network can further be reduced to two independent equations for the phase\u0000differences. By choosing appropriate coupling functions for the network, we can\u0000achieve desired synchronization dynamics regardless of the detailed properties\u0000of the limit-cycle oscillators used for the CPG. The effectiveness of our CPG\u0000network is demonstrated by numerical simulations of gait transitions between\u0000the wave, tetrapod, and tripod gaits, using the FitzHugh-Nagumo oscillator as\u0000the CPG unit.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140810139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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