 Thank you for giving me the floor before start my presentation I would like to thank the organizers of Jesus conference and it's the pleasure to me for me to To give a talk at this conference My name is more Tara morey Frankie. I'm the first and first year PhD student at University of Yawin the one in Cameroon Here Cameroon is a central Africa Here we have a unification monument, which is the history of the monument of Cameroon They have some traditional myths of Cameroon I belong to a research group who's the Supervisor is professor Jujie we received in 2018 the Elsevier Foundation Award for woman scientist in developing world The supervisor of my supervisor was professor Kofane We is received in 2014 the Kwame Kuma Continental Scientific Award We have many research access in our research group. We can have some some here Concerning stochastic processes we focus our research on Transport of particle in terms of stochastic resonance Many research paper have been published on this on stochastic resonance and is also in has also in the subject of PhD Defend by dr. Wadoop. We is currently the postdoctoral position in the University of Texas today I'll talk to you on recent research paper on stochastic resonance. It's about ghost stochastic resonance in an asymmetry g-fing Oceato the outline of this presentation is is as follow very very often the Dynamic of physical system is non-linear In physics and other science the a non-linear system is the opposite of a linear state That is the system that does not satisfy the supervision principle Which mean that the output is not directly proportional to the input for example a non-linear system You have a chaotic system or biological neural system What are linear or not? the We have the Phenomenon of resonance in most physical system Resonance describes the phenomenon of increase amplitude that will cure when the frequency of a applied pyrographic force Is bigger or close to a natural frequency of the system or which it acts We often Observe this phenomenon in bridges you have Many kind of resonance phenomenon and you can cite frequency resonance parametric resonance of vibrational resonance in addition when a dynamic system excite by both and pyrogic external force and noise The system can exit two other type of resonance namely stochastic resonance and ghost stochastic resonance Which is the subject of our presentation today? Let us talk about these two phenomena we start by Stochastic resonance Stochastic resonance is the amplification of weak signal at the output of non-linear system by argin noise This phenomenon was put forward by Roberto Benzi and Giorgio Parisi to explain the pyrogic recurring eye ages indeed In the Benzi and Parisi model global climate is Represented by a double world potential where a minimum represent a small temperature corresponding to a large portion of the herd covered by eyes the weak Modulation of the eccentricity of the health of it is represented by a weak pyrogic are forcing short-term climate filtration such as annual filtration in solar radiation a model by wide ocean noise if The noise is tuned so that the transition from cold to warm climate is synchronized It could significantly improve the response of herds climate to the small perturbation caused by eccentricity of herds of it after the introduction Stochastic resonance have found many application in many field such an economics electronics or biology Here we have the a general shame of stochastic resonance To have stochastic resonance at the output of the system It is necessary that the system must be no linear in all linear system at the input of the system You must have a weak signal and noise We observe the output performance and we talk about stochastic resonance when the output performance shows the Stochastic resonance peak at a critical noise intensity but however, if the pyrogic Signal at the input of a system is composed to many frequency You can have another type of stochastic Resonance nearly got stochastic resonance got to cut the illness is same is simply the Stochastic resonance which we observe at a frequency which doesn't exist at the input This phenomenon was put forward by shovel to explain how Sensory neuron perceive the periodicity of complete son Let us present now our objectives in this work We want to demonstrate the phenomenon of got stochastic resonance in an assembly teaching was here to excite by a Muti-frequency driving force and why Gaussian noise? We also want to show the influence of the assembly parameter of the appearance of the got stochastic resonance Here you have our model we consider it on the dark motion of Brown particle in three kind of assembly potential in presence of mutual frequency Force and additive noise the dimensionless dynamic equation of the particle correspond to it Do you think was later can be described as expression one in this expression F of tow is the Muti-frequency force which is a b-ammoni force composed of these frequencies 2 omega 0 and 2 omega 0 The additive noise is why Gaussian noise We've statistical preparation given by expression by expression 2 the particle move in the Asymmetric potential Here we have the shape of asymmetric potential Our potential is the double-whale potential Which depend to the asymmetric parameter? You can observe that the asymmetric parameter Control just the left wheel of of the potential the right way is constant And in the figure one the asymmetric parameter control only the depth of the left potential In the in figure one be the asymmetric parameter control only the width of The left wheel and if you go and see the Asymmetric parameter control see me turn use the depth and width of the left well We can defy the stochastic resonance by numerical calculate My creation at the output of our system the response given by expression six seven and and eight Let us now present our numerical result In order to reach our object which first define the parameter of of the system We perform our numerical strategies before order one scooter are going for stochastic processes developed by by customer Why Gaussian noise is produced numerically is the box molar formula The time step is zero point zero one and the initial velocity is zero We first study the response at the output of the system as a function of noise intensity At the frequency omega zero two omega zero and and three omega zero in the three kind of asymmetric potential We can see that we have A stochastic its stochastic resonance peak at these three frequency The stochastic resonance peak of safe at a frequency two omega zero and two omega zero is usual stochastic resonance But the stochastic resonance of in green of safety at the Omega zero is just the signature of ghost stochastic resonance in the system because The frequency omega zero is doesn't exist at the input of the system In order to have more information on this phenomenon in the system We study the power spectral density of the system and displacement of the particle We can see that the power spectral density display the eigen frequency of the of the system Although the power spectral density don't don't display the Missing frequency you can see that the particle evolves with the with the frequency in order to have information of So on influence of asymmetry in the system we plot the response As a function of noise and scientific for several value of asymmetry parameter And we see that There are so there are many value for which These ghost stochastic resonance occur in the system and when we increase the asymmetry parameter The ghost stochastic resonance phenomenon disappear gradually That is the figure one is the case of The depth asymmetry In the case of weight asymmetry We are we have many more value For which the ghost stochastic resonance occur in the system This allow us to tell that the weight asymmetry is more favorable to produce ghost stochastic resonance in our system We have done the the same work in the case of simultaneous weight and depth asymmetry In conclusion In this work, we have to we have investigate the ghost stochastic resonance phenomenon in three kinds of asymmetry Gfing was driven by white Gaussian noise And by a bm only force whose frequency are in The material of fundamental frequency omega zero The trigger the three asymmetry are namely the depth asymmetry weight asymmetry and simultaneous depth and weight asymmetry system In each asymmetry system there is a range of asymmetry parameter where ghost stochastic resonance Does occur and another range where the phenomenon become difficult to to induce So the occurrence of ghost stochastic resonance is controlled by asymmetry parameter in the in the system by compiling the influence of Three asymmetries And the response of the system is revealed that the weight asymmetry is the most favorable to the ghost stochastic resonance phenomenon This result significantly for optimal design and corresponding engineering application Thank you for your kind attention Thank you very much for the talk Are there any questions? First of all, I'm ignorant. So that's something that I have to say for just to start with so but I'm I was a bit confused by one fact. So you have a non-linear system And you inject a frequency which is two omega naught And three omega naught I would I mean Even without noise, I would expect To generate a signal at frequency omega naught So in this sense, I didn't quite understand if there is something peculiar Of the presence of the noise Or if it is something that you should have also without noise because when you inject the frequency on a linear system In general, if the non-linearity is generic, you generate all possible frequencies Although as I said, I'm ignorant. So maybe I'm even wrong I don't know In our system The SNR4 is a composite 2 If it is two frequency, two omega zero and two omega zero If you don't have noise, you can observe a Amplification of omega zero, but when we add noise Yes, but when we add noise on the system, I prefer the response on the output of the system So I think it's important to note that on the x-axis you have the temperature and you have a peak at a certain temperature So I think this is the resonance effect. So of course you have a periodic response of the system But he like you add noise, right? And then for a certain temperature You have a very strong response of the system and that's the resonance effect Yeah, exactly. So although your noise comes at all frequencies it picks the frequency of the yeah, okay Any more questions? Sometimes in stochastic resonance you estimate the performance by the signal to noise ratio, let's say So you compare without the periodic signal what happens and Yes Sometimes we we talk about stochastic resonance with signal to noise ratio, but in signal to noise ratio Is when we have the the the political force with one frequency When is the composed to two frequency is difficult to do a signal to noise ratio because in In the response We can we can observe if you want the resonance if resonance appear and And a at the frequency that we want You just we just replace the omega in the In the expression But we've seen that to know just is is difficult Um, I also have a question. So concerning this response So we saw that for some temperatures you have a negative response of the system, right? So the response curve was going to lower values as the temperature zero case. I think yeah Can you? Yeah, yeah, so for example here in the middle plot you can see the dip. Can you How do we have some intuition what happens for these temperatures? And what does it mean that the response is negative or like a smaller than temperature zero in deep we We work with dimers well as equation. So we just We just It's totally the response as a function of noise and strategy. Yes issues if you but In this when you see the statistical property of white Gaussian noise, we take all these KB the Department the temperature on intensity or the noise So Here we observe the Resonance peak ascent at a critical noise intensity. Yes. Yes. Okay. Yeah Okay, thank you Any more questions online? Okay, so if there are no more questions, then it's I think all of the speakers of the session You