patrick hervé louodop fotso - Academia.edu (original) (raw)

Papers by patrick hervé louodop fotso

Research paper thumbnail of A Mathematical Model of Tuberculosis with Drug Resistance Effects

Applied Mathematics, 2016

Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading... more Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant tuberculosis). In this work, we extend the standard SEIRS epidemiology model of tuberculosis to include MDR-TB. For that, we considered compartments of susceptible, exposed, infected, resistant to a first line of treatment and recovered humans and we modeled the natural growth, the interactions between these populations and the effects of treatments. We calculate the basic reproduction number, 0  , using the next generation method. The DFE and the EE are established and their stability analysis done to show that they are locally and globally asymptotically stable. Numerical analysis for the model with and without delay is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will still persist due to lack of permanent immunity to tuberculosis while the recovered can still lose their immunity to become susceptible again.

Research paper thumbnail of Erratum to: Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

Cognitive Neurodynamics, 2017

In the original publication of the article, the Acknowledgement has been missed out. It is given ... more In the original publication of the article, the Acknowledgement has been missed out. It is given in this erratum.

Research paper thumbnail of Chimera dynamics in an array of coupled FitzHugh-Nagumo system with shift of close neighbors

Heliyon

In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with close neighbors. Each e... more In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with close neighbors. Each element () connects to another () and its 2 neighbors. Shifting these neighbors produces particular phenomena such as chimera and multi-chimera. Step traveling chimera is observed for a time dependent shift. Results show that, basing oneself on both shift parameter and close neighbors , a full control on the chimera dynamics of the network can be ensured.

Research paper thumbnail of Dynamic Behavior of Pacemaker Models Subjected to a Arterial Pressure Excitation Simulator: Theoretical and Experimental Study by Microcontroller

Brazilian Journal of Physics, 2021

Research paper thumbnail of Nonlinear resonances phenomena in a modified Josephson junction model

Research paper thumbnail of Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

Physica Scripta, 2021

In this work, the dynamical behavior and real time control of a target trajectory of a modified V... more In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term sinnx is proposed. A generalization in the case of small oscillations on the sinnx function is studied. Due to sinnx function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge–Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results.

Research paper thumbnail of Nonlinear oscillators with state variable damping and elastic coefficients

Pramana, 2021

In the present work, we investigate the chaotic and limit-cycle behaviour of the new models of da... more In the present work, we investigate the chaotic and limit-cycle behaviour of the new models of damped nonlinear oscillators with elastic coefficients. The study concerning the stability of these models in their autonomous state presents periodical regions of stability and instability, a very rich dynamical behaviour. The analytical investigations on the existence of limit cycles show that a periodic solution (and therefore a limit cycle) in the ( x , y )-plane encompasses the origin. These models can be used to describe with some approximations, the artificial pacemaker. The chaos analysis shows the effect of state variable damping and elastic coefficient on the appearance of chaotic dynamics. Due to the complexity of the analogical functions, an experimental study was made by real implementation of an Arduino Card based on the Runge–Kutta algorithm of order 4. The results obtained show a good correlation with numerical results.

Research paper thumbnail of Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

Journal of Applied Mathematics and Physics, 2020

Research paper thumbnail of Chimera dynamics in an array of coupled FitzHugh-Nagumo system with shift of close neighbors

Heliyon, Apr 1, 2020

In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with R close neighbors. Each... more In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with R close neighbors. Each element (j) connects to another (m) and its 2R neighbors. Shifting these neighbors produces particular phenomena such as chimera and multi-chimera. Step traveling chimera is observed for a time dependent shift. Results show that, basing oneself on both shift parameter m and close neighbors R, a full control on the chimera dynamics of the network can be ensured.

Research paper thumbnail of Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array

Physical review. E, 2017

An array of excitable Josephson junctions under a global mean-field interaction and a common peri... more An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.

Research paper thumbnail of Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

Cognitive Neurodynamics, 2016

Research paper thumbnail of The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons

International Journal of Bifurcation and Chaos, 2014

In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-d... more In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh–Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.

Research paper thumbnail of Hartley’s oscillator: The simplest chaotic two-component circuit

Chaos, Solitons & Fractals, 2012

Research paper thumbnail of Chimera states in a neuronal network under the action of an electric field

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent section... more The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state and a multicluster traveling chimera.

Research paper thumbnail of Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic osc... more This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatio

Research paper thumbnail of Effective Synchronization of a Class of Chua’s Chaotic Systems Using an Exponential Feedback Coupling

Abstract and Applied Analysis, 2013

A robust exponential function based controller is designed to synchronize effectively a given cla... more A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.

Research paper thumbnail of Dynamics of multilayer networks with amplification

Chaos, 2020

We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Pr... more We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster, and chimera states. Here, we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of the chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain ...

Research paper thumbnail of Finite-time synchronization of tunnel-diode-based chaotic oscillators

Physical Review E, 2014

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic osc... more This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by PSPICE experiment are presented to show the feasibility of the proposed method.

Research paper thumbnail of A Mathematical Model of Tuberculosis with Drug Resistance Effects

Applied Mathematics, 2016

Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading... more Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant tuberculosis). In this work, we extend the standard SEIRS epidemiology model of tuberculosis to include MDR-TB. For that, we considered compartments of susceptible, exposed, infected, resistant to a first line of treatment and recovered humans and we modeled the natural growth, the interactions between these populations and the effects of treatments. We calculate the basic reproduction number, 0  , using the next generation method. The DFE and the EE are established and their stability analysis done to show that they are locally and globally asymptotically stable. Numerical analysis for the model with and without delay is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will still persist due to lack of permanent immunity to tuberculosis while the recovered can still lose their immunity to become susceptible again.

Research paper thumbnail of Erratum to: Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

Cognitive Neurodynamics, 2017

In the original publication of the article, the Acknowledgement has been missed out. It is given ... more In the original publication of the article, the Acknowledgement has been missed out. It is given in this erratum.

Research paper thumbnail of Chimera dynamics in an array of coupled FitzHugh-Nagumo system with shift of close neighbors

Heliyon

In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with close neighbors. Each e... more In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with close neighbors. Each element () connects to another () and its 2 neighbors. Shifting these neighbors produces particular phenomena such as chimera and multi-chimera. Step traveling chimera is observed for a time dependent shift. Results show that, basing oneself on both shift parameter and close neighbors , a full control on the chimera dynamics of the network can be ensured.

Research paper thumbnail of Dynamic Behavior of Pacemaker Models Subjected to a Arterial Pressure Excitation Simulator: Theoretical and Experimental Study by Microcontroller

Brazilian Journal of Physics, 2021

Research paper thumbnail of Nonlinear resonances phenomena in a modified Josephson junction model

Research paper thumbnail of Van der Pol equation with sine nonlinearity: dynamical behavior and real time control to a target trajectory

Physica Scripta, 2021

In this work, the dynamical behavior and real time control of a target trajectory of a modified V... more In this work, the dynamical behavior and real time control of a target trajectory of a modified Van der Pol model so the potential is proportional to the term sinnx is proposed. A generalization in the case of small oscillations on the sinnx function is studied. Due to sinnx function, the system presents periodical regions of stability and unstability, a very rich dynamical behavior. Analytical investigations based on the harmonic balance method came out some specific values of the excitation frequency for which the model is subjected to a phenomenon of frequency entrainment. Also, under effect of the sine function power, chaos appears for even small value of the nonlinearity coefficient, in contrast to the classical Van der Pol oscillator. An investigation as an artificial pacemaker is done based on the real frequency of the natural pacemaker. We found that the modified Van der Pol model, like the classic Van der Pol model, can play the role of an artificial pacemaker with some approximations. Due to the complexity of the analogical sine function, an experimental study was made by real implementation of an Arduino Card based on the Runge–Kutta 4th order algorithm. The results obtained show a good correlation with the numerical results.

Research paper thumbnail of Nonlinear oscillators with state variable damping and elastic coefficients

Pramana, 2021

In the present work, we investigate the chaotic and limit-cycle behaviour of the new models of da... more In the present work, we investigate the chaotic and limit-cycle behaviour of the new models of damped nonlinear oscillators with elastic coefficients. The study concerning the stability of these models in their autonomous state presents periodical regions of stability and instability, a very rich dynamical behaviour. The analytical investigations on the existence of limit cycles show that a periodic solution (and therefore a limit cycle) in the ( x , y )-plane encompasses the origin. These models can be used to describe with some approximations, the artificial pacemaker. The chaos analysis shows the effect of state variable damping and elastic coefficient on the appearance of chaotic dynamics. Due to the complexity of the analogical functions, an experimental study was made by real implementation of an Arduino Card based on the Runge–Kutta algorithm of order 4. The results obtained show a good correlation with numerical results.

Research paper thumbnail of Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

Journal of Applied Mathematics and Physics, 2020

Research paper thumbnail of Chimera dynamics in an array of coupled FitzHugh-Nagumo system with shift of close neighbors

Heliyon, Apr 1, 2020

In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with R close neighbors. Each... more In this paper, we consider an array of FitzHugh-Nagumo (FHN) systems with R close neighbors. Each element (j) connects to another (m) and its 2R neighbors. Shifting these neighbors produces particular phenomena such as chimera and multi-chimera. Step traveling chimera is observed for a time dependent shift. Results show that, basing oneself on both shift parameter m and close neighbors R, a full control on the chimera dynamics of the network can be ensured.

Research paper thumbnail of Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array

Physical review. E, 2017

An array of excitable Josephson junctions under a global mean-field interaction and a common peri... more An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.

Research paper thumbnail of Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

Cognitive Neurodynamics, 2016

Research paper thumbnail of The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons

International Journal of Bifurcation and Chaos, 2014

In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-d... more In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh–Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.

Research paper thumbnail of Hartley’s oscillator: The simplest chaotic two-component circuit

Chaos, Solitons & Fractals, 2012

Research paper thumbnail of Chimera states in a neuronal network under the action of an electric field

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent section... more The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state and a multicluster traveling chimera.

Research paper thumbnail of Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic osc... more This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatio

Research paper thumbnail of Effective Synchronization of a Class of Chua’s Chaotic Systems Using an Exponential Feedback Coupling

Abstract and Applied Analysis, 2013

A robust exponential function based controller is designed to synchronize effectively a given cla... more A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.

Research paper thumbnail of Dynamics of multilayer networks with amplification

Chaos, 2020

We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Pr... more We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster, and chimera states. Here, we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of the chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain ...

Research paper thumbnail of Finite-time synchronization of tunnel-diode-based chaotic oscillators

Physical Review E, 2014

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic osc... more This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by PSPICE experiment are presented to show the feasibility of the proposed method.