the optimality conditions of differentiable vector optimization problems abstract this paper deals with the differentiable vector optimization problems in the locally convex topological vector spaces we first establish a theorem of the alternative of the gordan type finally the optimality conditions of the kuhn tucker type are obtained

experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

optimality conditions for henig and globally proper efficient solutions with ordering cone has empty interior in this paper we consider the set valued vector optimization problems with constraint in locally convex spaces we present the necessary and sufficient conditions for henig efficient solution pair globally proper efficient solution pair and super efficient solution pair without the ordering cones having the nonempty interior

effect of non gaussian noise sources in a noise induced transition here we study a noise induced transition when the system is driven by a noise source taken as colored and non gaussian we show using both a theoretical approximation and numerical simulations that there is a shift of the transition as the noise departs from the gaussian behavior also we confirm the reentrance effect found for colored gaussian noise and show the behavior of the transition line in the phase like diagram as the noise departs from gaussianity in the large correlation time limit

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

existence theorems for set optimization problems abstract in this paper we consider set optimization problems by using a partial ordering based on a set relation we establish several existence results of minimal elements more general than those existing in the literature as an application we present sufficient conditions for the existence of solutions of a set valued optimization problem under some semi continuity assumption

global nontrivial bifurcation of homogeneous operators with an application to the p laplacian we prove the existence of a global solution branch of nontrivial solutions for a class of equations by a blow up method in particular positively homogeneous problems and equations with the p laplace operator are considered

continuity compactness and degree theory for operators in systems involving p laplacians and inclusions the study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in sobolev spaces we show that under natural assumptions this operator has the properties which allow to apply degree theory fixed point index for multivalued maps more precisely this operator is upper semicontinuous and compact with nonempty convex compact values for the particular case of systems involving p laplacians we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available

colored multiplicative and additive non gaussian noise driven dynamical system mean first passage time abstract we have studied the barrier crossing dynamics in presence of non gaussian noises it has been observed that multiplicative colored non gaussian noise can induce resonant activation ra the conspicuous dependence of mean first passage time mfpt on correlation time 2 of additive colored noise having fixed variance have been analyzed beyond a critical value of 2 the mfpt increases for a given rate of increase of noise strength with 2 if the additive colored noise is non gaussian the mfpt first decreases with increase of the non gaussian parameter measures deviation from gaussian character of multiplicative colored noise followed by an increase exhibiting a minimum the appearance of the minimum critically depends on the additive noise

two distinct mechanisms of coherence in randomly perturbed dynamical systems we carefully examine two mechanisms coherence resonance and self induced stochastic resonance by which small random perturbations of excitable systems with large time scale separation may lead to the emergence of new coherent behaviors in the form of limit cycles we analyze what controls the degree of coherence in these two mechanisms and classify their very different properties in particular we show that coherence resonance arises only at the onset of bifurcation and is rather insensitive against variations in the noise amplitude and the time scale separation ratio in contrast self induced stochastic resonance may arise away from bifurcations and the properties of the limit cycle it induces are controlled by both the noise amplitude and the time scale separation ratio

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

effects of non gaussian noise near supercritical hopf bifurcation abstract we have studied the effects of non gaussian colored noise in a chemical oscillation system the well known brusselator model in the parameter region close to the supercritical hopf bifurcation with the variation of the parameter q which quantifies the deviation from gaussian character the signal to noise ratio of noise induced oscillation exhibits a bell shaped change indicating the presence of resonant activity the cooperative effects of q and the correlation time on the performance of noise induced oscillation are also investigated interestingly resonance like behavior can be induced by either q or when the other parameter is properly fixed stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced this work provides us comprehensive understanding of how non gaussian noise influences the dynamics in chemical oscillation systems

global bifurcation for nonlinear equations abstract using a bifurcation result on noncompact branches of solutions in an abstract setting we establish the existence of global bifurcation for the following nonlinear equation div a u p 2 u 0 b u p 2 u q x u u subject to dirichlet boundary conditions under certain assumptions on a b and q when 0 is not an eigenvalue of the above divergence form

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

multiplicative stochastic resonance a multiplicative bistable stochastic system perturbed by a periodic forcing term is shown to exhibit stochastic resonance with increasing intensity of the multiplicative noise such an effect is related to the phenomenon of stochastic stabilization which takes place in the unperturbed system

duality for vector optimization of set valued functions in this note a general cone separation theorem between two subsets of image space is presented with the aid of this optimality conditions and duality for vector optimization of set valued functions in locally convex spaces are discussed

global bifurcation of the p laplacian and related operators abstract we prove some global bifurcation theorems of rabinowitz type for a large class of operators the results apply in particular to equations involving the p laplacian

properties of resonant activation phenomena the phenomenon of resonant activation of a brownian particle over a fluctuating barrier is revisited we discuss the important distinctions between barriers that can fluctuate among up and down configurations and barriers that are always up but that can fluctuate among different heights a resonance as a function of the barrier fluctuation rate is found in both cases but the nature and physical description of these resonances is quite distinct the nature of the resonances the physical basis for the resonant behavior and the importance of boundary conditions are discussed in some detail we obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate and show that our analytic results are in excellent agreement with numerical results s1063 651x 98 11304 1

coherence resonance induced by non gaussian noise in a deterministic hodgkin huxley neuron in this paper we report a novel effect of a particular kind of non gaussian noise ngn especially its deviation from gaussian noise on the spiking activity in a deterministic hodgkin huxley hh neuron it is found via numerical simulations that the coefficient of variation cv characterizing the spiking regularity nonlinearly changes with varying deviation and passes through a minimum at an optimal deviation value representing the presence of the coherence resonance cr this phenomenon shows that when the ngn is optimal the neuron can exhibit the most regular firing behavior this result provides a constructive role of the ngn in the timing precision of information processing and signal transduction in neural systems

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

stochastic system with coupling between non gaussian and gaussian noise terms a stochastic system with coupling between non gaussian and gaussian noise terms is investigated a general approximate fokker planck equation of the system is derived through a path integral approach for a bistable system the coupling between noise terms can induce the reentrance like phase transition while the parameter q of the departure from the gaussian noise can induce the first order like phase transition both the coupling and the parameter q can change the curve of the mean first passage time mfpt from monotonically decreasing function to a peak in the mfpt numerical simulations are carried out to check the approximate theoretical results reasonably good agreement is obtained

asymmetric probability densities in symmetrically modulated bistable devices a brownian particle hopping in a symmetric double well potential can be statistically confined into a single well by the simultaneous action of a two periodic input signals one tilting the minima and the other one modulating the barrier height and b an additive and a purely multiplicative random signal generated by a unique source and thus preserving a certain degree of statistical correlation the underlying gating mechanism is quite robust when compared for instance with biharmonic rocking in view of technological implementation asymmetric confinement through gating can be conveniently maximized by tuning the input signal parameters correlation time phase time lag amplitudes thus revealing a resonant localization mechanism of general applicability

resonant activation in a bistable system the analog simulation of an overdamped brownian particle in a quartic double well potential driven by an external either gaussian or dichotomic multiplicative noise is performed with special focus on the phenomenon of resonant activation such an effect is shown to occur on increasing the correlation time of the multiplicative noise while keeping the noise variance constant the asymptotic behavior of the relevant escape times for large noise correlation time and large variance is also investigated simple qualitative arguments are produced to justify the results thus obtained furthermore the traversal barrier that is the effective barrier at the time the system switches state is shown to have a minimum for a certain value of the noise correlation time though not always in coincidence with the relevant resonant activation value textcopyright 1996 the american physical society

optimization of set valued functions abstract let x y and z be real topological vector spaces and e c x be a convex set c y d z are to be pointed convex cones let f x 2y be c convex and g x 2z be d convex set valued functions we consider the problems formula this paper generalizes the moreau rockafellar type theorem and the farkas minkowski type theorem for set valued functions when y r n and z r m we established the necessary and sufficient conditions for the existence of geoffrion efficient solution of p and the relationship between the proper efficient solutions and geoffrion efficient solutions of p the mond weir type and wolfe type vector duality theorems are also considered in this paper

chaotic states in a random world relationship between the nonlinear differential equations of excitability and the stochastic properties of ion channels excitable membranes allow cells to generate and propagate electrical signals in the nervous system these signals transmit information in muscle they trigger contraction and in heart they regulate spontaneous beating a central question in excitability theory concerns the relationship between the aggregate properties of membranes marcoscopic and the properties of channels in the membranes mircoscopic hodgkin and huxley 1952 laid the foundations of membrane excitability and neher and sakmann 1976 developed techniques to study individual channels this article focuses on the relationship between the macroscopic domain in which non linear differential equations determine the electrical properties of cells and the microscopic domain in which the probabilistic nature of channels establishes the pattern of activity using nerve cell membranes as an example we examine how information in one domain predicts behavior in the other we conclude that the probabilistic nature of channels generates virtually all macroscopic electrical properties including resting potentials action potentials spontaneous firing and chaos

a global bifurcation for nonlinear inclusions abstract for under certain conditions we show a global bifurcation for multi valued boundary value problems involving the laplacian by applying a bifurcation theorem for nonlinear inclusions

optimality conditions for a nonconvex set valued optimization problem in this paper we study necessary and sufficient optimality conditions for a set valued optimization problem convexity of the multifunction and the domain is not required a definition of k approximating multifunction is introduced this multifunction is the differentiability notion applied to the problem a characterization of weak minimizers is obtained for invex and generalized k convexlike multifunctions using the lagrange multiplier rule

generalized constraint qualifications and optimality conditions for set valued optimization problems in this paper we discuss the connections of four generalized constraint qualifications for set valued vector optimization problems with constraints then some k t type necessary and sufficient optimality conditions are derived in terms of the contingent epiderivatives

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

the optimality conditions for vector optimization of set valued maps this paper deals with the minimization problems of set valued maps in the real linear spaces first a theorem of the alternative for the subconvexlike set valued maps is established using the separation theorem of convex sets in a real linear space finally the optimality conditions for vector optimization of set valued maps are obtained

degree and global bifurcation for elliptic equations with multivalued unilateral conditions abstract a bifurcation problem for an elliptic multivalued boundary value problem with a real parameter is considered the existence of global bifurcation between two eigenvalues of a certain type of the laplacian is proved for a class of abstract inclusions with compact multivalued mappings in a hilbert space it is shown how the degree can be determined near the eigenvalues of a particular type of an associated linear single valued problem and the jump of the degree is proved as a consequence global bifurcation for such abstract inclusions is obtained the weak formulation of the boundary value problem mentioned is a particular case