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2. Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event.

Author

Khalil, Kamal, Lanza, Valentina, Manceau, David, Aziz-Alaoui, M. A., and Provitolo, Damienne

Subjects
*POPULATION dynamics
Abstract

In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection–diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and L 1 -boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios. [ABSTRACT FROM AUTHOR]

Published
2024
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3. Modeling and Analysis of the Impact of Risk Culture on Human Behavior during a Catastrophic Event

Author

Lanza, Valentina, Provitolo, Damienne, Verdière, Nathalie, Bertelle, Cyrille, Dubos-Paillard, Edwige, Navarro, Oscar, Charrier, Rodolphe, Mikiela, Irmand, Aziz-Alaoui, Moulay, Boudoukha, Abdel, Tricot, Anne, Schleyer-Lindenmann, Alexandra, Berred, Alexandre, Haule, Sébastien, Tric, Emmanuel, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes (LITIS), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Psychologie des Pays de la Loire (LPPL), Université d'Angers (UA)-Nantes Université - UFR Lettres et Langages (Nantes Univ - UFR LL), Nantes Université - pôle Humanités, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Humanités, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Études des Structures, des Processus d’Adaptation et des Changements de l’Espace (ESPACE), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Avignon Université (AU)-Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR, and ANR-17-CE39-0008,Com2SiCa,COMprendre et SImuler les COMportements humains sur des territoires en situation de CAtastrophe : de l'analyse à l'anticipation(2017)

Subjects
human behaviors, [SDV.NEU.PC]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Psychology and behavior, disaster, mathematical modeling, [SHS.GEO]Humanities and Social Sciences/Geography, [MATH]Mathematics [math], human behaviors mathematical modeling disaster risk management, risk management, [SHS]Humanities and Social Sciences
Abstract

International audience; In a world more and more affected by natural and/or industrial disasters, it is essential to understand, analyze and control human behavior during such events. The work presented in this article is one of the results of a transdisciplinary collaboration between geographers, psychologists, mathematicians, computer scientists, operational staff and stakeholders in risk management. This collaboration made it possible to identify the diverse behavioral reactions that can occur during a disaster and to propose a categorization of these behavioral states and their transitions. These behavioral dynamics are described by the APC (Alert-Panic-Control) mathematical model, which integrates two key elements (among others) during disasters: cognition and social contagion. Several scenarios are developed, and a qualitative analysis of the model is conducted to better understand the role of crowd density and risk culture on behavioral dynamics.; Dans un monde de plus en plus touché par les catastrophes naturelles et/ou industrielles, il est essentiel de comprendre, d'analyser et de maîtriser les comportements humains lors de tels événements. Le travail présenté dans cet article est l'un des résultats d'une collaboration transdisciplinaire entre géographes, psychologues, mathématiciens, informaticiens, opérationnels et acteurs de la gestion des risques. Cette collaboration a permis d'identifier les diverses réactions comportementales pouvant survenir lors d'une catastrophe et de proposer une catégorisation de ces états comportementaux et de leurs transitions. Ces dynamiques comportementales sont décrites par le modèle mathématique APC (Alerte-Panique-Contrôle), qui intègre deux éléments clés (parmi d'autres) lors de catastrophes : la cognition et la contagion sociale. Plusieurs scénarios sont développés et une analyse qualitative du modèle est menée pour mieux comprendre le rôle de la densité de la foule et de la culture du risque sur la dynamique comportementale.

Published
2023
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4. Study of the Effect of Rescuers and the Use of a Massive Alarm in a Population in a Disaster Situation

Author

Verdière, Nathalie, Dubos-Paillard, Edwige, Lanza, Valentina, Provitolo, Damienne, Charrier, Rodolphe, Bertelle, Cyrille, Berred, Alexandre, Tricot, Anne, Aziz-Alaoui, Moulay, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes (LITIS), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Études des Structures, des Processus d’Adaptation et des Changements de l’Espace (ESPACE), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Avignon Université (AU)-Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR, and ANR-17-CE39-0008,Com2SiCa,COMprendre et SImuler les COMportements humains sur des territoires en situation de CAtastrophe : de l'analyse à l'anticipation(2017)

Subjects
[SDV.NEU.PC]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Psychology and behavior, [SHS.GEO]Humanities and Social Sciences/Geography, [MATH]Mathematics [math], catastrophic event, emergency and risk management, human behavior, mathematical model, simulations, optimal control
Abstract

Faced with an ongoing or imminent danger, crisis managers must do their utmost to protect the exposed population and limit the extent of the disaster. More than during the pre- and post-disaster phases, time is of the essence. This temporal specificity of the disaster is essential compared to the risk. It requires a perfect coordination and a quick response in a context of uncertainty. It is important to intervene rapidly on the scene of the disaster while ensuring there are enough first responders. Crisis managers must also quickly alert the population at risk in order to favor the adoption of protective behaviors and limit inappropriate reactions, panic phenomena, and the spread of rumors. In France, in the event of a danger affecting the population, the intervention of law enforcement and emergency services is relatively rapid, even though there may be differences depending on the territories (urban or rural). On the contrary, the triggering of the alert by institutional actors (the mayor or the prefect, depending on the extent of the disaster) must follow a strict procedure that imposes longer delays and may limit or even neutralize its effectiveness. This article proposes a theoretical reflection on the effectiveness of these two types of intervention (relief and warning) with affected populations in the case of rapid kinetic or unpredictable events affecting people with a low risk culture. This reflection is based on the mathematical model “alert, panic, control” (APC) inspired by models used in epidemiology. It enables the modeling of behavior dynamics by distinguishing control and panic behaviors resulting from the difficulty or incapacity to regulate emotions. Several scenarios are proposed to identify the phases during which these two kinds of intervention have an optimal effect on the population by limiting panic phenomena.

Published
2023
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6. A theoretical reflection on temporal aspects of emergency population warning and rescue response on human behaviors during disasters

Author

Dubos-Paillard, Edwige, Tricot, Anne, Verdière, Nathalie, Lanza, Valentina, Provitolo, Damienne, Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université Paris 1 Panthéon-Sorbonne (UP1), Études des Structures, des Processus d’Adaptation et des Changements de l’Espace (ESPACE), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Avignon Université (AU)-Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Aix Marseille Université (AMU), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Normandie Université (NU), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Université Côte d'Azur (UCA), and ANR-17-CE39-0008,Com2SiCa,COMprendre et SImuler les COMportements humains sur des territoires en situation de CAtastrophe : de l'analyse à l'anticipation(2017)

Subjects
warning, disaster, human behavior, mathematical modelling, PARIS team, [SHS.GEO]Humanities and Social Sciences/Geography, relief, [MATH]Mathematics [math], COM, [SHS]Humanities and Social Sciences
Abstract

International audience; During disasters, people, confronted by life-threatening situations, deal with high levels of stress. While some groups of individuals will be able to cope and adopt thoughtful responses, others will experience acute stress reactions that will disrupt their psychological and physiological functioning leading to irrational responses such as terror, agitation or panic flight (Chidiac & Crocq, 2010). These last reactions are difficult to manage for the emergency services. They often require early assistance provided by medico-psychological emergency cells. Several factors can influence people’s reactions in face with a disaster. Beyond the intensity, the frequency, the temporality and the spatiality of the event (Dubos-Paillard et al, 2021), some factors such as education, risk culture, preparedness can influence the human toll of the disaster. This paper proposes a theoretical reflection on two factors: the diffusion of information via a warning system reaching a large number of individuals (Douvinet, 2020) and a more localized but on-site intervention by the police and rescue services. We assume that they can influencepositively the dynamics of behavior during the event, but that their effectiveness depends on the period in which they are implemented. We base our reflection on a dynamic multi-compartments model, the Alert-Panic-Control (APC) model, which allows to model the diversity of human behaviors and their evolution during a disaster (Provitolo et al, 2015; Lanza et al, 2020; Verdiere et al, 2021). Inspired by epidemiological models, it makes it possible to simulate different scenarios in which the population can evolve between three kinds of behaviors named Alert (awareness of the danger), Control (sheltering, evacuation, etc.) and Panic (disordered agitation, panic flight, etc.). The objective is therefore to estimate the best moments to implement these two solutions, considering uneven levels of efficiency in order to limit potential “panic” behaviors.

Published
2022

7. A meta-population network on geographical maps to simulate population behaviors during a catastrophic event

Author

Charrier, Rodolphe, Lanza, Valentina, Provitolo, Damienne, Verdière, Nathalie, Dubos-Paillard, Edwige, Bertelle, Cyrille, Equipe Réseaux d'interactions et Intelligence Collective (RI2C - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Géographie-cités (GC (UMR_8504)), and Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)

Subjects
PARIS team, COM, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

11. Optimal strategies to control human behaviors during a catastrophic event.

Author

Mikiela, Irmand, Lanza, Valentina, Verdière, Nathalie, and Provitolo, Damienne

Subjects
MAXIMUM principles (Mathematics), OPTIMAL control theory, HUMAN behavior, EMERGENCY management, EMOTIONAL state
Abstract

In a world the more and more affected by sudden, unpredictable natural and/or industrial disasters, with few or without warning signs, it is essential to understand, analyze and control population behaviors during such events. Our objective is to model and investigate the actions that can be deployed by operational staff during catastrophic events in order to optimize risk management, reduce panic and save lives. For this purpose, we propose and solve an optimal control problem by using Pontryagin's Maximum Principle. Finally, we determine the best control strategy in the realistic scenario of a tsunami on the French Riviera. [ABSTRACT FROM AUTHOR]

Published
2022
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12. On the application of the describing function technique to the bifurcation analysis of nonlinear systems

Author

Lanza, Valentina, Bonnin, Michele, and Gilli, Marco

Subjects
Linear systems -- Analysis, Oscillators (Electronics) -- Usage, Business, Computers and office automation industries, Electronics, Electronics and electrical industries
Abstract

Spectral techniques, like harmonic balance, are classical numerical tools for designing nonlinear oscillators and microwave circuits. Recently these techniques have been exploited for investigating complex dynamics in nonlinear systems. In this manuscript we firstly show that limit cycle Floquet's multipliers and the related bifurcation phenomena can be estimated through a spectral approach, entirely based on the describing function technique. Then we consider some significant case studies, and we show that our method yields more accurate results than the other describing function-based approaches proposed in the literature. Index Terms--Bifurcation, describing function, limit cycles, nonlinear systems.

Published
2007

15. Blinking Networks of Memristor Oscillatory Circuits in the Flux-Charge Domain.

Author

Lanza, Valentina, Secco, Jacopo, and Corinto, Fernando

Subjects
INVARIANT manifolds, TOPOLOGICAL property, NONLINEAR oscillators, FAST fashion, SYNCHRONIZATION
Abstract

Multistability phenomena and complex nonlinear dynamics in memristor oscillators pave the way to obtain efficient solutions to optimization problems by means of novel computational architectures based on the interconnection of single–device oscillators. It is well-known that topological properties of interconnections permit to control synchronization and spatio–temporal patterns in oscillatory networks. When the interconnections can change in time with a given probability to connect two oscillators, the whole network acts as a complex network with blinking couplings. The work of has shown that a particular class of blinking complex networks are able to completely synchronize in a faster fashion with respect to other coupling strategies. This work focuses on the specific class of blinking complex networks made of Memristor–based Oscillatory Circuits (MOCs). By exploiting the recent Flux–Charge Analysis Method, we make clear that synchronization phenomena in blinking networks of memristor oscillators having stochastic couplings, i.e., Blinking Memristor Oscillatory Networks (BMONs), correspond to global periodic oscillations on invariant manifolds and the effect of a blinking link is to shift the nonlinear dynamics through the infinite (invariant) manifolds. Numerical simulations performed on MOCs prove that synchronization phenomena can be controlled just by changing the coupling amongst them. [ABSTRACT FROM AUTHOR]

Published
2021
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16. Control of panic behavior in a non identical network coupled with a geographical model

Author

Cantin, Guillaume, Aziz-Alaoui, M, Verdière, Nathalie, Lanza, Valentina, Charrier, Rodolphe, Bertelle, Cyrille, Provitolo, Damienne, Dubos-Paillard, Edwige, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Equipe Réseaux d'interactions et Intelligence Collective (RI2C - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université Le Havre Normandie (ULH), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Géoazur (GEOAZUR 7329), Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université de Rouen Normandie (UNIROUEN), Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA), Université Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris, ANR: 15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Université Panthéon-Sorbonne (UP1)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), CANTIN, Guillaume, and Idex UCA JEDI - - UCA JEDI2015 - ANR-15-IDEX-0001 - IDEX - VALID

Subjects
[SHS.GEO] Humanities and Social Sciences/Geography, panic, [MATH] Mathematics [math], PARIS team, [SHS.GEO]Humanities and Social Sciences/Geography, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, coupled network, bifurcation, Control, [INFO]Computer Science [cs], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH]Mathematics [math], COM, synchronization
Abstract

International audience; In this paper, our aim is to study the control of panic behavior in a non-identical network coupled with a model for human behaviors during catastrophic events, and to establish the link between control and synchronization of the network. We show how to model the domino effect in the case of a succession of disasters and exhibit a Hopf bifurcation. We explore the patterns emerging from basic two-nodes configurations and analyze the effect of the coupling strength on the bifurcations that occur in the subsequent dynamical system. We illustrate our qualitative results by a numerical simulation of a specific catastrophe, prepared with the collaboration of geographers.

Published
2017

17. MULTIPLE HOPF BIFURCATIONS IN COUPLED NETWORKS OF PLANAR SYSTEMS

Author

Cantin , Guillaume, Aziz-Alaoui , M, Verdière , Nathalie, Lanza , Valentina, Laboratoire de Mathématiques Appliquées du Havre ( LMAH ), Université Le Havre Normandie ( ULH ), Normandie Université ( NU ) -Normandie Université ( NU ), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), and Normandie Université (NU)-Normandie Université (NU)

Subjects
[ MATH ] Mathematics [math], ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Hamiltonian system, Melnikov coefficients, Hopf bifurcation, Limit cycle, [MATH]Mathematics [math], coupled network
Abstract

International audience; In this communication, we study coupled networks built with non-identical instances of a dynamical system exhibiting a Hopf bifurcation. We first show how the coupling generates the birth of multiple limit cycles. Next, we project those coupled networks in the real plane, and construct a polynomial Hamiltonian system of degree n, admitting O(n 2) non-degenerate centers. We explore various perturbations of that Hamiltonian system and implement an algorithm for the symbolic computation of the Melnikov coefficients.

Published
2017

18. Identifiability, Integro-Differential Equations and Neurobiology. Talk Afternotes

Author

Boulier, François, Lemaire, François, Poteaux, Adrien, Quadrat, Alban, Verdière, Nathalie, Corson, Nathalie, Lanza, Valentina, Castel, Hélène, Gandolfo, Pierrick, Compère, Vincent, Gérardin, Emmanuel, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Institut National de la Santé et de la Recherche Médicale (INSERM), Différenciation et communication neuronale et neuroendocrine (DC2N), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Institut National de la Santé et de la Recherche Médicale (INSERM), Service d'imagerie médicale [CHU Rouen], Hôpital Charles Nicolle [Rouen], CHU Rouen, Normandie Université (NU)-Normandie Université (NU)-CHU Rouen, Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU), and Boulier, François

Subjects
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], [SDV.BIBS] Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], neurobiology, modeling, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, integro-differential equations, identifiability, computer algebra, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; This talk presents an interdisciplinary research project mixing computer algebra (Lille), applied mathematics and modeling (Le Havre) and neurobiology (Rouen). This document was obtained by merging the slides of the talk and an ``ideal'' version of the speech, synthetized after the talk.

Published
2017

20. Judeo-Arabic Orthographies: Insights from a Fifteenth-Century Šarḥ.

Author

Lanza, Valentina Bella

Subjects
JUDEO-Arabic language, DIALECTS, ORTHOGRAPHY & spelling, MANUSCRIPTS, LINGUISTIC analysis
Abstract

Judeo-Arabic is a religiolect that developed as a result of the great Arab-Islamic conquests during the 7th century. This linguistic variety shares some of those features common to Neoarabic dialects; nonetheless, it preserves its own uniqueness, such as the almost absolute use of Hebrew characters and the occurrence of Hebrew and Aramaic lexical and grammatical elements within the texts. The writing system of Judeo-Arabic was affected by the socio-political changes that occurred during its development. In particular, Judeo-Arabic was subjected to a dramatic change during the 15th century, as a result of the increasing isolation of the Jews. In this period the so-called 'Hebraized' orthography became more prevalent and turned out to be representative of the šurūḥ , i.e. Judeo-Arabic translations of Hebrew sacred texts. In this contribution, we will focus on the issue of Judeo-Arabic graphic adaptation, through the linguistic analysis of an unpublished manuscript from the 15th century containing a šarḥ. Peculiarities and potential inconsistencies are discussed according to the wider and renowned Judeo-Arabic orthographic classification. [ABSTRACT FROM AUTHOR]

Published
2020
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21. Understanding and Simulation of Human Behaviors in Areas Affected by Disasters: From the Observation to the Conception of a Mathematical Model

Author

Verdière, Nathalie, Cantin, Guillaume, Provitolo, Damienne, Lanza, Valentina, Dubos-Paillard, Edwige, Charrier, Rodolphe, Aziz-Alaoui, Moulay, Bertelle, Cyrille, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7), Equipe Réseaux d'interactions et Intelligence Collective (RI2C - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), and Normandie Université (NU)

Subjects
Systemic modeling, Differential equation, Disaster, Human behavior, Mathematical modeling, Panic, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; One of the major challenges today is to better understand and anticipate both individual and collective human behaviors face to threats and disasters, whatever their causes. This anticipation is the critical point for populations and operational services in charge of managing the crisis, since it helps ensure populations’ safety and keep the emergency situation under control as well as its spatial and temporal spread. This paper deals with the modeling of the temporal dynamics of human behaviors during a catastrophic event. Several complex models, at different scales, can be found in the literature in order to model crowd dynamics. Up to now, the models essentially take into account the panic since it is the most feared reaction. However, human sciences learn us that the population during a catastrophic event can exhibit different concurrent reactions, as behavioral sequences, and each individual does not keep the same behavior. A first work associating geographers, mathematicians, computer scientists has been proposed in this direction (Verdière et al., 2014; Provitolo et al., 2015). They have developed a first SIRbased model considering three different types of collective behaviors in catastrophic event and their different interactions. In this paper, we propose a more mature version of the mathematical model (called PCR for « Panic / Controlled and Reflex behaviors) simulating the behavioral sequences from a first phase called « reflex » to a second phase called « rational » according to the type of the threat, domino-effects and local environment.

Published
2015

22. Understanding and simulation of human behaviors in areas affected by disasters : from the observation to theconception of a mathematical mode

Author

Verdière, Nathalie, Cantin, Guillaume, Provitolo, Damienne, Lanza, Valentina, Dubos-Paillard, Edwige, Charrier, Rodolphe, Aziz-Alaoui, Moulay, Bertelle, Cyrille, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Géographie-cités (GC (UMR_8504)), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7), Equipe Réseaux d'interactions et Intelligence Collective (RI2C - LITIS), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU), Provitolo, Damienne, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), and Université Paris 1 Panthéon-Sorbonne (UP1)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SHS.GEO] Humanities and Social Sciences/Geography, [INFO]Computer Science [cs], [MATH] Mathematics [math], [SHS.GEO]Humanities and Social Sciences/Geography, [INFO] Computer Science [cs], [MATH]Mathematics [math], Human behavior, Panic, Disaster, Systemic modeling, Mathematical modeling, Differential equation
Abstract

International audience; One of the major challenges today is to better understand and anticipate both individual and collective human behaviors face to threats and disasters, whatever their causes. This anticipation is the critical point for populations and operational services in charge of managing the crisis, since it helps ensure populations’ safety and keep the emergency situation under control as well as its spatial and temporal spread. This paper deals with the modeling of the temporal dynamics of human behaviors during a catastrophic event. Several complex models, at different scales, can be found in the literature in order to model crowd dynamics. Up to now, the models essentially take into account the panic since it is the most feared reaction. However, human sciences learn us that the population during a catastrophic event can exhibit different concurrent reactions, as behavioral sequences, and each individual does not keep the same behavior. A first work associating geographers, mathematicians, computer scientists has been proposed in this direction (Verdière et al., 2014; Provitolo et al., 2015). They have developed a first SIRbased model considering three different types of collective behaviors in catastrophic event and their different interactions. In this paper, we propose a more mature version of the mathematical model (called PCR for « Panic / Controlled and Reflex behaviors) simulating the behavioral sequences from a first phase called « reflex » to a second phase called « rational » according to the type of the threat, domino-effects and local environment.

Published
2015

23. Mathematical modeling of human behaviors during catastrophic events

Author

Verdière, Nathalie, Lanza, Valentina, Charrier, Rodolphe, Provitolo, Damienne, Dubos-Paillard, Edwige, Bertelle, Cyrille, Alaoui, Aziz, Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Université Le Havre Normandie (ULH), Normandie Université (NU), Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA), Géographie-cités (GC (UMR_8504)), Université Panthéon-Sorbonne (UP1)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), projet PEPS interdisciplinaire HuMaIn, Normandie Université (NU)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Université Paris 1 Panthéon-Sorbonne (UP1)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Université de Rouen Normandie (UNIROUEN), and Verdière, Nathalie

Subjects
[SHS.GEO] Humanities and Social Sciences/Geography, catastrophic event, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Modeling, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], human behavior, [SHS.GEO]Humanities and Social Sciences/Geography
Abstract

International audience; In this paper, we introduce a new approach for modeling the human collective behaviors in the specific scenario of a sudden catastrophe, this catastrophe can be natural (i.e. earthquake, tsunami) or technological (nuclear event). The novelty of our work is to propose a mathematical model taking into account different concurrent behaviors in such situation and to include the processes of transition from one behavior to the other during the event. Thus, in this multidisciplinary research included mathematicians, computer scientists and geographers, we take into account the psychological reactions of the population in situations of disasters, and study their propagation mode. We propose a SIR-based model, where three types of collective reactions occur in catastrophe situations: reflex, panic and controlled behaviors. Moreover, we suppose that the interactions among these classes of population can be realized through imitation and emotional contagion processes. Some simulations will attest the relevance of the proposed model.

Published
2014

25. Emergence of synchronization in bio-inspired artificial neural network memristor-coupled oscillatory cells

Author

Ascoli, Alon, Lanza, Valentina, Corinto, Fernando, Tetzlaff, Ronald, Technische Universität Dresden ( TUD ), Laboratoire de Mathématiques Appliquées du Havre ( LMAH ), Université Le Havre Normandie ( ULH ), Normandie Université ( NU ) -Normandie Université ( NU ), Dipartimento di Elettronica e Telecomunicazioni [Turin] ( DET ), Politecnico di Torino [Torino] ( Polito ), Technische Universität Dresden = Dresden University of Technology (TU Dresden), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Dipartimento di Elettronica e Telecomunicazioni [Torino] (DET), and Politecnico di Torino = Polytechnic of Turin (Polito)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2014

29. Mathematical Modeling of Human Behaviors During Catastrophic Events: Stability and Bifurcations.

Author

Cantin, Guillaume, Verdiére, Nathalie, Lanza, Valentina, Aziz-Alaoui, M. A., Charrier, Rodolphe, Bertelle, Cyrille, Provitolo, Damienne, and Dubos-Paillard, Edwige

Subjects
HUMAN behavior, CATASTROPHIC illness, BIFURCATION theory, PREDICTION models, BEHAVIOR evolution
Abstract

The aim of this paper is to present some mathematical results concerning the PCR system (Panic-Control-Reflex), which is a model for human behaviors during catastrophic events. This model has been proposed to better understand and predict human reactions of individuals facing a brutal catastrophe, in a context of an established increase of natural and industrial disasters. After stating some basic properties, that is positiveness, boundedness, and stability of the solutions, we analyze the transitional dynamic. We then focus on the bifurcation that occurs in the system, when one behavioral evolution parameter passes through a critical value. We exhibit a degeneracy case of a saddle-node bifurcation, in a larger context of classical saddle-node bifurcations and saddle-node bifurcations at infinity, and we study the inhibition effect of higher order terms. [ABSTRACT FROM AUTHOR]

Published
2016
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32. Phase model reduction for oscillatory networks subject to stochastic inputs.

Author

Bonnin, Michele, Corinto, Fernando, and Lanza, Valentina

Abstract

Oscillatory networks represent a circuit architecture for image and information processing, that can be used to realize associative and dynamic memories. Phase noise is often a limiting key factors for the performances of oscillatory networks. The ideal framework to investigate phase noise effect in nonlinear oscillators are phase models. Classical phase models lead to the conclusion that, in presence of random disturbances such as white noise, the phase noise problem is simply a diffusion process. In this paper we develop a reduced order model for phase noise analysis in nonlinear oscillators. We derive a reduced Fokker-Planck equation for the phase variable and the corresponding reduced phase equations. We show that the phase noise problem is a convection-diffusion process, proving that white noise produces both phase diffusion and frequency shift. [ABSTRACT FROM PUBLISHER]

Published
2012
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33. MULTIPLE ATTRACTORS AND BIFURCATIONS IN HARD OSCILLATORS DRIVEN BY CONSTANT INPUTS.

Author

LANZA, VALENTINA, PONTA, LINDA, BONNIN, MICHELE, and CORINTO, FERNANDO

Subjects
*ATTRACTORS (Mathematics), *BIFURCATION theory, *DYNAMICAL systems, *LAGRANGIAN points, *LIMIT cycles, *NONLINEAR oscillators
Abstract

Hard oscillators are dynamical systems that show the coexistence of qualitatively different attractors, in the form of limit cycles and equilibrium points. In the presence of external inputs their dynamic behavior is significantly different from those of oscillators, called soft, with a limit cycle as unique attractor. This paper studies the dynamics of a simple hard oscillator under the influence of a constant external input. It is shown that, despite the apparent simplicity, when the input strength and the oscillator's natural frequency are varied the system exhibits many different bifurcation phenomena, including global bifurcations as saddle-node on limit cycle and homoclinic bifurcations. The model under investigation can play a role in neuroscience, as it exhibits two different mechanisms of class I neural excitability and one mechanism for class II. It also highlights a mechanism of transition between the two classes. [ABSTRACT FROM AUTHOR]

Published
2012
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34. LOCALIZED OSCILLATIONS IN DIFFUSIVELY COUPLED CYCLIC NEGATIVE FEEDBACK SYSTEMS.

Author

LANZA, VALENTINA, CORINTO, FERNANDO, and GILLI, MARCO

Subjects
*LOCALIZATION theory, *OSCILLATIONS, *FEEDBACK control systems, *SYSTEMS biology, *CELL differentiation, *GLOBAL analysis (Mathematics), *COMPLEXITY (Philosophy)
Abstract

Oscillations in networks composed of Cyclic Negative Feedback systems (CNF systems) are widely used to mimic many periodic phenomena occurring in systems biology. In particular, the possible coexistence of different attractors permits to suitably describe the differentiating processes arising in living cells. The aim of the manuscript is to characterize, through a spectral based technique, the complex global dynamical behaviors emerging in arrays of diffusively coupled CNF systems. [ABSTRACT FROM AUTHOR]

Published
2012
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37. Localized oscillations in diffusively coupled cyclic negative feedback systems

Author

Valentina Lanza, Marco Gilli, Fernando Corinto, Department of Electronics [Torino] (DELEN), Politecnico di Torino = Polytechnic of Turin (Polito), and Lanza, Valentina

Subjects
Regulatory genetic networks, bio-inspired systems, discrete breathers, Physics, 0209 industrial biotechnology, Applied Mathematics, Systems biology, 020208 electrical & electronic engineering, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, 020901 industrial engineering & automation, Control theory, Modeling and Simulation, Negative feedback, Attractor, 0202 electrical engineering, electronic engineering, information engineering, Statistical physics, Engineering (miscellaneous), ComputingMilieux_MISCELLANEOUS
Abstract

Oscillations in networks composed of Cyclic Negative Feedback systems (CNF systems) are widely used to mimic many periodic phenomena occurring in systems biology. In particular, the possible coexistence of different attractors permits to suitably describe the differentiating processes arising in living cells. The aim of the manuscript is to characterize, through a spectral based technique, the complex global dynamical behaviors emerging in arrays of diffusively coupled CNF systems.

Published
2011

38. Bifurcations in simple genetic cycle models

Author

Valentina Lanza, Fernando Corinto, Marco Gilli, Department of Electronics [Torino] (DELEN), Politecnico di Torino = Polytechnic of Turin (Polito), and Lanza, Valentina

Subjects
Equilibrium point, 0303 health sciences, 0209 industrial biotechnology, Systems biology, Mathematical analysis, Ode, 02 engineering and technology, 03 medical and health sciences, 020901 industrial engineering & automation, Simple (abstract algebra), Limit cycle, Attractor, Statistical physics, ComputingMilieux_MISCELLANEOUS, Bifurcation, 030304 developmental biology, Mathematics, Repressilator
Abstract

In order to describe genetic regulatory networks several deterministic models based on systems of nonlinear ordinary differential equations (ODEs) have been proposed. The Elowitz repressilator, modeled as a system of three genes that repress each other in a ring, is one of the most outstanding examples. Furthermore, systems that can display a coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. The aim of the manuscript is to investigate the global periodic oscillations and their bifurcations in networks composed of simple bio-inspired oscillators that have a stable limit cycle and equilibrium point, separated by an unstable limit cycle.

Published
2010

39. On the application of the describing function technique to the bifurcation analysis of nonlinear systems

Author

Marco Gilli, Valentina Lanza, Michele Bonnin, Department of Mathematics [Torino] (DIMAT), Politecnico di Torino = Polytechnic of Turin (Polito), Department of Electronics [Torino] (DELEN), and Lanza, Valentina

Subjects
Floquet theory, 020208 electrical & electronic engineering, Mathematical analysis, Describing function, 02 engineering and technology, 01 natural sciences, Nonlinear system, Complex dynamics, Harmonic balance, Limit cycle, 0103 physical sciences, Signal Processing, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Electrical and Electronic Engineering, 010301 acoustics, Bifurcation, ComputingMilieux_MISCELLANEOUS, Electronic circuit, Mathematics
Abstract

Spectral techniques, like harmonic balance, are classical numerical tools for designing nonlinear oscillators and microwave circuits. Recently these techniques have been exploited for investigating complex dynamics in nonlinear systems. In this manuscript we firstly show that limit cycle Floquet's multipliers and the related bifurcation phenomena can be estimated through a spectral approach, entirely based on the describing function technique. Then we consider some significant case studies, and we show that our method yields more accurate results than the other describing function-based approaches proposed in the literature

Published
2007

40. Analysis of nonlinear oscillatory network dynamics via time-varying amplitude and phase variables

Author

Fernando Corinto, Marco Gilli, Pier Paolo Civalleri, Valentina Lanza, Lanza, Valentina, Department of Mathematics [Torino] (DIMAT), Politecnico di Torino = Polytechnic of Turin (Polito), and Department of Electronics [Torino] (DELEN)

Subjects
Applied Mathematics, 020208 electrical & electronic engineering, Dynamics (mechanics), Phase (waves), 020206 networking & telecommunications, 02 engineering and technology, Network dynamics, Computer Science Applications, Electronic, Optical and Magnetic Materials, Set (abstract data type), Nonlinear system, Harmonic balance, Amplitude, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Electrical and Electronic Engineering, ComputingMilieux_MISCELLANEOUS, Electronic circuit, Mathematics
Abstract

The goal of this manuscript is to propose a method for investigating the global dynamics of nonlinear oscillatory networks, with arbitrary couplings. The procedure is mainly based on the assumption that the dynamics of each oscillator is accurately described by a couple of variables, that is, the oscillator periodic orbits are represented through time-varying amplitude and phase variables. The proposed method allows one to derive a set of coupled nonlinear ordinary differential equations governing the time-varying amplitude and phase variables. By exploiting these nonlinear ordinary differential equations, the prediction of the total number of periodic oscillations and their bifurcations is more accurate and simpler with respect to the one given by the latest available methodologies. Furthermore, it is proved that this technique also works for weakly connected oscillatory networks. Finally, the method is applied to a chain of third-order oscillators (Chua's circuits) and the results are compared with those obtained via a numerical technique, based on the harmonic balance approach. Copyright © 2007 John Wiley & Sons, Ltd.

Published
2007

41. Exogenous control of vascular network formation in vitro: a mathematical model

Author

Valentina Lanza, Luigi Preziosi, Davide Carlo Ambrosi, Lanza, Valentina, Department of Mathematics [Torino] (DIMAT), and Politecnico di Torino = Polytechnic of Turin (Polito)

Subjects
Statistics and Probability, 0303 health sciences, Computer science, Applied Mathematics, Regeneration (biology), General Engineering, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, 03 medical and health sciences, Vascular network, 0101 mathematics, Biological system, ComputingMilieux_MISCELLANEOUS, 030304 developmental biology
Abstract

The reconstitution of a proper and functional vascular network is a major issue in tissue engineering and regeneration. The limited success of current technologies may be related to the difficulties to build a vascular tree with correct geometric ratios for nutrient delivery. The present paper develops a mathematical model suggesting how an anisotropic vascular network can be built in vitro by using exogenous chemoattractant and chemorepellent. The formation of the network is strongly related to the nonlinear characteristics of the model.

Published
2006

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