We study the phenomenon of multistability in mutualistic networks of plants and pollinators, where one desired state in which all species coexist competes with multiple states in which some species are gone extinct. In this setting, we examine the relation between the endangerment of pollinator species and their position within the mutualistic network. To this end, we compare endangerment rankings which are derived from the species' probabilities of going extinct due to random shock perturbations with rankings obtained from different network theoretic centrality metrics. We find that a pollinator's endangerment is strongly linked to its degree of mutualistic specialization and its position within the core-periphery structure of its mutualistic network, with the most endangered species being specialists in the outer periphery. Since particularly well established instances of such peripheral areas are tree-shaped structures which stem from links between nodes/species in the outermost shell of the network, we summarized our findings in the admittedly ambiguous slogan 'keep the bees off the trees'. Finally, we challenge the generality of our findings by testing whether the title of this work still applies when being located in the outer periphery allows pollinators to avoid competitive pressure.
{"title":"Keep the bees off the trees: The particular vulnerability of species in the periphery of mutualistic networks to shock perturbations","authors":"Lukas Halekotte, Anna Vanselow, Ulrike Feudel","doi":"arxiv-2403.02085","DOIUrl":"https://doi.org/arxiv-2403.02085","url":null,"abstract":"We study the phenomenon of multistability in mutualistic networks of plants\u0000and pollinators, where one desired state in which all species coexist competes\u0000with multiple states in which some species are gone extinct. In this setting,\u0000we examine the relation between the endangerment of pollinator species and\u0000their position within the mutualistic network. To this end, we compare\u0000endangerment rankings which are derived from the species' probabilities of\u0000going extinct due to random shock perturbations with rankings obtained from\u0000different network theoretic centrality metrics. We find that a pollinator's\u0000endangerment is strongly linked to its degree of mutualistic specialization and\u0000its position within the core-periphery structure of its mutualistic network,\u0000with the most endangered species being specialists in the outer periphery.\u0000Since particularly well established instances of such peripheral areas are\u0000tree-shaped structures which stem from links between nodes/species in the\u0000outermost shell of the network, we summarized our findings in the admittedly\u0000ambiguous slogan 'keep the bees off the trees'. Finally, we challenge the\u0000generality of our findings by testing whether the title of this work still\u0000applies when being located in the outer periphery allows pollinators to avoid\u0000competitive pressure.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036585","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}
Using a model of the FitzHugh-Nagumo oscillator in the excitable regime, we investigate the influence of the L'evy noise's properties on the effect of coherence resonance. In particular, we demonstrate that the L'evy noise can be a constructive or destructive factor providing for enhancement or suppression of noise-induced coherence. We show that the positive or negative role of the L'evy noise impact is dictated by the noise's stability index and skewness parameter. The correlation time and the deviation of interspike intervals used in this analysis are shown to be maximized or minimized for an appropriate choice of the noise parameters. Numerical simulations are combined with experiments on an electronic circuit showing an excellent qualitative correspondence and proving thereby the robustness of the observed phenomena.
{"title":"Lévy noise-induced coherence resonance in the FitzHugh-Nagumo oscillator: numerical study versus experiment","authors":"Ivan Korneev, Anna Zakharova, Vladimir V. Semenov","doi":"arxiv-2402.19426","DOIUrl":"https://doi.org/arxiv-2402.19426","url":null,"abstract":"Using a model of the FitzHugh-Nagumo oscillator in the excitable regime, we\u0000investigate the influence of the L'evy noise's properties on the effect of\u0000coherence resonance. In particular, we demonstrate that the L'evy noise can be\u0000a constructive or destructive factor providing for enhancement or suppression\u0000of noise-induced coherence. We show that the positive or negative role of the\u0000L'evy noise impact is dictated by the noise's stability index and skewness\u0000parameter. The correlation time and the deviation of interspike intervals used\u0000in this analysis are shown to be maximized or minimized for an appropriate\u0000choice of the noise parameters. Numerical simulations are combined with\u0000experiments on an electronic circuit showing an excellent qualitative\u0000correspondence and proving thereby the robustness of the observed phenomena.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006844","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}
Koichiro Yawata, Kai Fukami, Kunihiko Taira, Hiroya Nakao
We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.
{"title":"Phase autoencoder for limit-cycle oscillators","authors":"Koichiro Yawata, Kai Fukami, Kunihiko Taira, Hiroya Nakao","doi":"arxiv-2403.06992","DOIUrl":"https://doi.org/arxiv-2403.06992","url":null,"abstract":"We present a phase autoencoder that encodes the asymptotic phase of a\u0000limit-cycle oscillator, a fundamental quantity characterizing its\u0000synchronization dynamics. This autoencoder is trained in such a way that its\u0000latent variables directly represent the asymptotic phase of the oscillator. The\u0000trained autoencoder can perform two functions without relying on the\u0000mathematical model of the oscillator: first, it can evaluate the asymptotic\u0000phase and phase sensitivity function of the oscillator; second, it can\u0000reconstruct the oscillator state on the limit cycle in the original space from\u0000the phase value as an input. Using several examples of limit-cycle oscillators,\u0000we demonstrate that the asymptotic phase and phase sensitivity function can be\u0000estimated only from time-series data by the trained autoencoder. We also\u0000present a simple method for globally synchronizing two oscillators as an\u0000application of the trained autoencoder.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115180","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}
Vassilis Papadopoulos, Guilhem Doat, Arthur Renard, Clément Hongler
One key challenge in Artificial Life is designing systems that display an emergence of complex behaviors. Many such systems depend on a high-dimensional parameter space, only a small subset of which displays interesting dynamics. Focusing on the case of continuous systems, we introduce the 'Phase Transition Finder'(PTF) algorithm, which can be used to efficiently generate parameters lying at the border between two phases. We argue that such points are more likely to display complex behaviors, and confirm this by applying PTF to Lenia showing it can increase the frequency of interesting behaviors more than two-fold, while remaining efficient enough for large-scale searches.
{"title":"Looking for Complexity at Phase Boundaries in Continuous Cellular Automata","authors":"Vassilis Papadopoulos, Guilhem Doat, Arthur Renard, Clément Hongler","doi":"arxiv-2402.17848","DOIUrl":"https://doi.org/arxiv-2402.17848","url":null,"abstract":"One key challenge in Artificial Life is designing systems that display an\u0000emergence of complex behaviors. Many such systems depend on a high-dimensional\u0000parameter space, only a small subset of which displays interesting dynamics.\u0000Focusing on the case of continuous systems, we introduce the 'Phase Transition\u0000Finder'(PTF) algorithm, which can be used to efficiently generate parameters\u0000lying at the border between two phases. We argue that such points are more\u0000likely to display complex behaviors, and confirm this by applying PTF to Lenia\u0000showing it can increase the frequency of interesting behaviors more than\u0000two-fold, while remaining efficient enough for large-scale searches.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006833","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}
The widespread development and use of neural networks have significantly enriched a wide range of computer algorithms and promise higher speed at lower cost. However, the imitation of neural networks by means of modern computing substrates is highly inefficient, whereas physical realization of large scale networks remains challenging. Fortunately, delayed-feedback oscillators, being much easier to realize experimentally, represent promising candidates for the empirical implementation of neural networks and next generation computing architectures. In the current research, we demonstrate that coupled bistable delayed-feedback oscillators emulate a multilayer network, where one single-layer network is connected to another single-layer network through coupling between replica nodes, i.e. the multiplex network. We show that all the aspects of the multiplexing impact on wavefront propagation and stochastic resonance identified in multilayer networks of bistable oscillators are entirely reproduced in the dynamics of time-delay oscillators. In particular, varying the coupling strength allows suppressing and enhancing the effect of stochastic resonance, as well as controlling the speed and direction of both deterministic and stochastic wavefront propagation. All the considered effects are studied in numerical simulations and confirmed in physical experiments, showing an excellent correspondence and disclosing thereby the robustness of the observed phenomena.
{"title":"Delayed-feedback oscillators replicate the dynamics of multiplex networks: wavefront propagation and stochastic resonance","authors":"Anna Zakharova, Vladimir V. Semenov","doi":"arxiv-2402.16551","DOIUrl":"https://doi.org/arxiv-2402.16551","url":null,"abstract":"The widespread development and use of neural networks have significantly\u0000enriched a wide range of computer algorithms and promise higher speed at lower\u0000cost. However, the imitation of neural networks by means of modern computing\u0000substrates is highly inefficient, whereas physical realization of large scale\u0000networks remains challenging. Fortunately, delayed-feedback oscillators, being\u0000much easier to realize experimentally, represent promising candidates for the\u0000empirical implementation of neural networks and next generation computing\u0000architectures. In the current research, we demonstrate that coupled bistable\u0000delayed-feedback oscillators emulate a multilayer network, where one\u0000single-layer network is connected to another single-layer network through\u0000coupling between replica nodes, i.e. the multiplex network. We show that all\u0000the aspects of the multiplexing impact on wavefront propagation and stochastic\u0000resonance identified in multilayer networks of bistable oscillators are\u0000entirely reproduced in the dynamics of time-delay oscillators. In particular,\u0000varying the coupling strength allows suppressing and enhancing the effect of\u0000stochastic resonance, as well as controlling the speed and direction of both\u0000deterministic and stochastic wavefront propagation. All the considered effects\u0000are studied in numerical simulations and confirmed in physical experiments,\u0000showing an excellent correspondence and disclosing thereby the robustness of\u0000the observed phenomena.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980217","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}
Phatthamon Kongkhambut, Jayson G. Cosme, Jim Skulte, Michelle A. Moreno Armijos, Ludwig Mathey, Andreas Hemmerich, Hans Keßler
Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the drive, while CTCs are driven continuously and oscillate with a system inherent frequency. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequency $omega_mathrm{CTC}$ is prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequency $omega_{mathrm{dr}}$ close to $2,omega_mathrm{CTC}$ leads to robust locking of $omega_mathrm{CTC}$ to $omega_{mathrm{dr}}/2$, and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.
{"title":"Observation of a phase transition from a continuous to a discrete time crystal","authors":"Phatthamon Kongkhambut, Jayson G. Cosme, Jim Skulte, Michelle A. Moreno Armijos, Ludwig Mathey, Andreas Hemmerich, Hans Keßler","doi":"arxiv-2402.12378","DOIUrl":"https://doi.org/arxiv-2402.12378","url":null,"abstract":"Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical\u0000many-body states, that are characterized by robust self-sustained oscillations,\u0000emerging via spontaneous breaking of discrete or continuous time translation\u0000symmetry. DTCs are periodically driven systems that oscillate with a\u0000subharmonic of the drive, while CTCs are driven continuously and oscillate with\u0000a system inherent frequency. Here, we explore a phase transition from a\u0000continuous time crystal to a discrete time crystal. A CTC with a characteristic\u0000oscillation frequency $omega_mathrm{CTC}$ is prepared in a continuously\u0000pumped atom-cavity system. Modulating the pump intensity of the CTC with a\u0000frequency $omega_{mathrm{dr}}$ close to $2,omega_mathrm{CTC}$ leads to\u0000robust locking of $omega_mathrm{CTC}$ to $omega_{mathrm{dr}}/2$, and hence\u0000a DTC arises. This phase transition in a quantum many-body system is related to\u0000subharmonic injection locking of non-linear mechanical and electronic\u0000oscillators or lasers.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920715","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}
Collective motion provides a spectacular example of self-organization in Nature. Visual information plays a crucial role among various types of information in determining interactions. Recently, experiments have revealed that organisms such as fish and insects selectively utilize a portion, rather than the entirety, of visual information. Here, focusing on fish, we propose an agent-based model where the direction of attention is guided by visual stimuli received from the images of nearby fish. Our model reproduces a branching phenomenon where a fish selectively follows a specific individual as the distance between two or three nearby fish increases. Furthermore, our model replicates various patterns of collective motion in a group of agents, such as vortex, polarized school, swarm, and turning. We also discuss the topological nature of visual interaction, as well as the positional distribution of nearby fish and the map of pairwise and three-body interactions induced by them. Through a comprehensive comparison with existing experimental results, we clarify the roles of visual interactions and issues to be resolved by other forms of interactions.
{"title":"Selective decision making and collective behavior of fish by the motion of visual attention","authors":"Susumu Ito, Nariya Uchida","doi":"arxiv-2402.09073","DOIUrl":"https://doi.org/arxiv-2402.09073","url":null,"abstract":"Collective motion provides a spectacular example of self-organization in\u0000Nature. Visual information plays a crucial role among various types of\u0000information in determining interactions. Recently, experiments have revealed\u0000that organisms such as fish and insects selectively utilize a portion, rather\u0000than the entirety, of visual information. Here, focusing on fish, we propose an\u0000agent-based model where the direction of attention is guided by visual stimuli\u0000received from the images of nearby fish. Our model reproduces a branching\u0000phenomenon where a fish selectively follows a specific individual as the\u0000distance between two or three nearby fish increases. Furthermore, our model\u0000replicates various patterns of collective motion in a group of agents, such as\u0000vortex, polarized school, swarm, and turning. We also discuss the topological\u0000nature of visual interaction, as well as the positional distribution of nearby\u0000fish and the map of pairwise and three-body interactions induced by them.\u0000Through a comprehensive comparison with existing experimental results, we\u0000clarify the roles of visual interactions and issues to be resolved by other\u0000forms of interactions.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771810","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}
Fernando E. Rosas, Bernhard C. Geiger, Andrea I Luppi, Anil K. Seth, Daniel Polani, Michael Gastpar, Pedro A. M. Mediano
Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled.
{"title":"Software in the natural world: A computational approach to emergence in complex multi-level systems","authors":"Fernando E. Rosas, Bernhard C. Geiger, Andrea I Luppi, Anil K. Seth, Daniel Polani, Michael Gastpar, Pedro A. M. Mediano","doi":"arxiv-2402.09090","DOIUrl":"https://doi.org/arxiv-2402.09090","url":null,"abstract":"Understanding the functional architecture of complex systems is crucial to\u0000illuminate their inner workings and enable effective methods for their\u0000prediction and control. Recent advances have introduced tools to characterise\u0000emergent macroscopic levels; however, while these approaches are successful in\u0000identifying when emergence takes place, they are limited in the extent they can\u0000determine how it does. Here we address this limitation by developing a\u0000computational approach to emergence, which characterises macroscopic processes\u0000in terms of their computational capabilities. Concretely, we articulate a view\u0000on emergence based on how software works, which is rooted on a mathematical\u0000formalism that articulates how macroscopic processes can express self-contained\u0000informational, interventional, and computational properties. This framework\u0000establishes a hierarchy of nested self-contained processes that determines what\u0000computations take place at what level, which in turn delineates the functional\u0000architecture of a complex system. This approach is illustrated on paradigmatic\u0000models from the statistical physics and computational neuroscience literature,\u0000which are shown to exhibit macroscopic processes that are akin to software in\u0000human-engineered systems. Overall, this framework enables a deeper\u0000understanding of the multi-level structure of complex systems, revealing\u0000specific ways in which they can be efficiently simulated, predicted, and\u0000controlled.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771877","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}
Sebastian EydamRIKEN Center for Brain Science, Igor FranovićInstitute of Physics Belgrade, Louis KangRIKEN Center for Brain Science
We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation analysis of a three-dimensional mean-field system derived in the framework of next-generation neural mass models allows us to explain the scenarios and suggest control strategies for the transitions between the neurophysiologically desired asynchronous states and the synchronous, seizure-like states featuring collective oscillations. We reveal two qualitatively different scenarios for the onset of synchrony. For weaker couplings, a bistability region between the lower- and the higher-activity asynchronous states unfolds from the cusp point, and the collective oscillations emerge via a supercritical Hopf bifurcation. For stronger couplings, one finds seven co-dimension two bifurcation points, including pairs of Bogdanov-Takens and generalized Hopf points, such that both lower- and higher-activity asynchronous states undergo transitions to collective oscillations, with hysteresis and jump-like behavior observed in vicinity of subcritical Hopf bifurcations. We demonstrate three control mechanisms for switching between asynchronous and synchronous states, involving parametric perturbation of the adenosine triphosphate (ATP) production rate, external stimulation currents, or pulse-like ATP shocks, and indicate a potential therapeutic advantage of hysteretic scenarios.
我们考虑了一种异质的、全局耦合的兴奋性四元整合-发射神经元群，这种神经元群的兴奋性因与生酮饮食（一种癫痫治疗方法）相关的代谢反馈而发生适应性变化。在下一代神经质量模型的框架内衍生出的三维均场系统的分岔分析使我们能够解释这些情况，并为神经生理学所需的异步状态和以集体振荡为特征的同步癫痫发作样状态之间的过渡提出控制策略。我们揭示了同步开始的两种定性不同的情况。对于弱耦合，低活性和高活性同步状态之间的双稳态区域从尖点开始展开，集体振荡通过超临界霍普夫分岔出现。对于强耦合，我们发现了七个共维二分岔点，包括一对波格丹诺夫-塔肯斯点和广义霍普夫点，这样低活度和高活度异步态都会过渡到集体振荡，在次临界霍普夫分岔点附近会观察到滞后和跳跃行为。我们展示了在异步态和同步态之间切换的三种控制机制，涉及三磷酸腺苷（ATP）产生率的参数扰动、外部刺激电流或脉冲式 ATP 冲击，并指出了滞后情景的潜在治疗优势。
{"title":"Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet","authors":"Sebastian EydamRIKEN Center for Brain Science, Igor FranovićInstitute of Physics Belgrade, Louis KangRIKEN Center for Brain Science","doi":"arxiv-2402.04388","DOIUrl":"https://doi.org/arxiv-2402.04388","url":null,"abstract":"We consider a heterogeneous, globally coupled population of excitatory\u0000quadratic integrate-and-fire neurons with excitability adaptation due to a\u0000metabolic feedback associated with ketogenic diet, a form of therapy for\u0000epilepsy. Bifurcation analysis of a three-dimensional mean-field system derived\u0000in the framework of next-generation neural mass models allows us to explain the\u0000scenarios and suggest control strategies for the transitions between the\u0000neurophysiologically desired asynchronous states and the synchronous,\u0000seizure-like states featuring collective oscillations. We reveal two\u0000qualitatively different scenarios for the onset of synchrony. For weaker\u0000couplings, a bistability region between the lower- and the higher-activity\u0000asynchronous states unfolds from the cusp point, and the collective\u0000oscillations emerge via a supercritical Hopf bifurcation. For stronger\u0000couplings, one finds seven co-dimension two bifurcation points, including pairs\u0000of Bogdanov-Takens and generalized Hopf points, such that both lower- and\u0000higher-activity asynchronous states undergo transitions to collective\u0000oscillations, with hysteresis and jump-like behavior observed in vicinity of\u0000subcritical Hopf bifurcations. We demonstrate three control mechanisms for\u0000switching between asynchronous and synchronous states, involving parametric\u0000perturbation of the adenosine triphosphate (ATP) production rate, external\u0000stimulation currents, or pulse-like ATP shocks, and indicate a potential\u0000therapeutic advantage of hysteretic scenarios.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771533","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}
Many important systems in nature are characterized by oscillations. To understand and interpret such behavior, researchers use the language of mathematical models, often in the form of differential equations. Nowadays, these equations can be derived using data-driven machine learning approaches, such as the white-box method 'Sparse Identification of Nonlinear Dynamics' (SINDy). In this paper, we show that to ensure the identification of sparse and meaningful models, it is crucial to identify the correct position of the system limit cycle in phase space. Therefore, we propose how the limit cycle position and the system's nullclines can be identified by applying SINDy to the data set with varying offsets, using three model evaluation criteria (complexity, coefficient of determination, generalization error). We successfully test the method on an oscillatory FitzHugh-Nagumo model and a more complex model consisting of two coupled cubic differential equations. Finally, we demonstrate that using this additional side information on the limit cycle in phase space can improve the success of model identification efforts in oscillatory systems.
{"title":"Data-driven reconstruction of limit cycle position provides side information for improved model identification with SINDy","authors":"Bartosz Prokop, Nikita Frolov, Lendert Gelens","doi":"arxiv-2402.03168","DOIUrl":"https://doi.org/arxiv-2402.03168","url":null,"abstract":"Many important systems in nature are characterized by oscillations. To\u0000understand and interpret such behavior, researchers use the language of\u0000mathematical models, often in the form of differential equations. Nowadays,\u0000these equations can be derived using data-driven machine learning approaches,\u0000such as the white-box method 'Sparse Identification of Nonlinear Dynamics'\u0000(SINDy). In this paper, we show that to ensure the identification of sparse and\u0000meaningful models, it is crucial to identify the correct position of the system\u0000limit cycle in phase space. Therefore, we propose how the limit cycle position\u0000and the system's nullclines can be identified by applying SINDy to the data set\u0000with varying offsets, using three model evaluation criteria (complexity,\u0000coefficient of determination, generalization error). We successfully test the\u0000method on an oscillatory FitzHugh-Nagumo model and a more complex model\u0000consisting of two coupled cubic differential equations. Finally, we demonstrate\u0000that using this additional side information on the limit cycle in phase space\u0000can improve the success of model identification efforts in oscillatory systems.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771532","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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